







Trig functions and the unit circle 
20141002 

From Jake: I was wondering what conclusions can be drawn about the trigonometric functions and how they work about the circle. Can you also please give me an explanation for it? Thank you. Answered by Penny Nom. 





Cutting a round cake so that it doesn't dry out 
20140826 

From James: I'm wondering if there's a simple way to calculate the area between two parallel chords of a circle equidistant from its diameter, or if I have the area, to find the distance between the two chords.
Here's my "problem". You may have heard of the way of cutting a round cake so that it doesn't dry out  make two parallel cuts (chords) the length of the cake, take the middle piece, then push the two pieces together.
So I know the area of a 12" cake, and I want say, exactly an eighth of the cake. How wide do I cut the centre piece?
Now to get even more difficult, the next day I want another eighth from the centre. How wide do I cut the next pieces, and so on...?
Thanks,
James Answered by Harley Weston. 





An arc subtended at the center of the Earth 
20140720 

From Abhinav: Meerut is 60 km from Delhi. Find the nearest second the angle subtended at the center of the earth by the arc joining these two points,earth being regarded as a sphere of 5940 km radius. Answered by Penny Nom. 





Solve sin3x = cos2x 
20140714 

From Emanuel: If sin3x=cos2x, find the value of x when x<0<90' Answered by Penny Nom. 





An antenna is atop a building 
20140705 

From Andrew: If an antenna is atop a building 70 feet tall and the antenna has a beamwidth of 30 degrees how far from the building does the beam first touch the ground? Answered by Penny Nom. 





The height of a building 
20140517 

From Jim: If I'm 150 ft. from the base of a building and the top of the building is approx. at a 75 degree angle, how do you calculate the height? Answered by Penny Nom. 





x  2 Sin[x] = 0 
20140508 

From chanmy: please help me to sole this equation x  2 Sin[x] = 0,thank you Answered by Penny Nom. 





2cos^2x+cosx=sin^2x 
20140428 

From MaryBeth: find all solutions of the following equation in the interval [0,pi]
2cos^x+cosx=sin^2x Answered by Robert Dawson. 





A triangular chicken pen 
20140427 

From Cierra: Margaret has two lengths of fence, 20 meters and 24 meters, for two sides of a triangular chicken pen. The third side will be on the north side of the barn. One fence length makes a 75° angle with the barn. How many different pens can she build if one fence is attached at the corner of the barn? What are all the possible lengths for the barn side of the pen?
Not sure what they are asking here... please show step by step what to do! Thank you so much! Answered by Penny Nom. 





Solve for theta 
20140425 

From ALASTAIR: Hi, The question asks Solve for 'theta' cos2theta=sintheta x costheta.
Substituting for cos2th either 12sin^2th or 2cos^2th does not give an equation in either sine or cosine alone how do I solve this please? Answered by Penny Nom. 





An octagonal pad 
20140425 

From George: Hi,
I need to pour a cement pad in the shape of an octagon that allows
for 12" of clearance around the tank I will be putting on it.
The tank has a radius of 16'. Answered by Penny Nom. 





A trig problem 
20140425 

From srishti: Consider the points P= (sin(ab),cosa), Q=(cos(ab),sina), R=(cos(ab+c),sin(ac), where 0 Answered by Chris Fisher. 





The cosine of 2 theta 
20140410 

From Kayla: Find \cos 2 \theta if \sin \theta = \frac{11}{61}. Answered by Robert Dawson. 





Cutting a hexagon from a disk 
20140405 

From Paul: I am a machinist and sometimes need to make a hex from
round material.
If I know the distance of the flat sides opposite one another
of my hex, how can I calculate the size of material I need to turn
to give me the right diameter to finish the part with six sides? Answered by Penny Nom. 





A trig expression 
20140331 

From Al: the question is Find the value of sq rt 1cos40/
1+cos40( that is the square root of the numerator and denominator)
I can't see what the question is about or even less an obvious answer Can anybody help? Answered by Chris Fisher. 





The area of a 5 sided lot 
20140315 

From Michael: Question from michael:
This lot is in feet. 59x154x109x188x137 per the plot plan Answered by Harley Weston. 





The angle of depression 
20140308 

From Ranger_minor: A woman of height 1.4 metres standing
on the top of a building 34.6 metres high
views a tree some distance away.
she observes that the angle of depression of the bottom of the tree
is 35 degrees and the angle of depression of the top of the tree
is 29 degrees.
assume that the building and the tree are on level ground :
1). calculate the distance of the woman
from the top of the tree measured along her line of sight. Answered by Penny Nom. 





A limit with trig functions 
20140222 

From pearl: (what is the value of limit of x as it approaches 0 of sin8x divided by cos6x) Answered by Penny Nom. 





A trig identity 
20140121 

From Jhosseline: prove: sin (pi/2  x) cot (x + pi/2)= sinx Answered by Penny Nom. 





Radio direction finders 
20140109 

From Nathan: Radio direction finders set up two points A and B, which are 2.5 miles
apart on an eastwest line. From A, it is found that the bearing of a
signal from a radio transmitter is N36.33 degress E, while from B the
bearing of the same signal is N53.67 degrees W. Find the distance of
the transmitter from B. Answered by Penny Nom. 





conical lamp stand/staved wood 
20131207 

From Henry: need to make lamp stand that is wooden staved; need it to be 25 inches at bottom and 10 inches at top; need to know angles for staves to be cut; the lamp stand will be rounded on a lathe and will be 40 inches tall John Lucas built one and it is pictured on his web page. thank you for any help/direction; I checked out the answered for cone shaped objects on your page but didn't find what I could use. thanks again. Henrywoodturner, parent teacher student . . . . . Answered by Harley Weston. 





2cos(2A)=2^1/2 
20131114 

From Mary: Solve the following trigonometric equation over 0 being less than or equal to A but less than 2pie
2cos(2A)=2^1/2 Answered by Penny Nom. 





Using trig to find the height of a hill 
20130814 

From Anna: From the top of a hill, the angles of depression of two successive milestones on a level road, which leads straight away from the hill, are 5degrees and 15degrees respectively. Fine the height of the hill.
Suggestion: BE is drawn perpendicular to AD. Find BE, then BD, finally CD.
Thanks :) Answered by Penny Nom. 





Practical uses of trigonometry 
20130806 

From tharindu: use of trigonometry Answered by Penny Nom. 





The angle of elevation of the sun 
20130703 

From Maurice: A vertical pole with a length of 7m cast a shadow with a length of 5m. Calculate the angle of elevation of the sun and include a diagram. Answered by Penny Nom. 





A kennel for a beagle 
20130603 

From david: Hi, I'm building some beagle kennels and I am in need of help with an angle problem. I need to place a roof on my kennel with a drop of 2inches across 3ft 10inches. the posts on the right side will be 5ft and the post on the left will be 4ft 10in. the posts are 4x4 and the space to be covered is 3ft 10in from the outside of the 4x4. Please help, thanks. Answered by Penny Nom. 





Inverse trig functions 
20130519 

From ky: hello, so iv'e been asked to draw a triangle with sides of 3, 4, and 5.
And find the measure of all three angle using sin1, cos1, tan1.
I got really confuse, I'm taking the SAT pretty soon and it would be great
to get this... THANX Answered by Penny Nom. 





(4 4cos^4 x)/(sin^2 x) 
20130518 

From Agnes: How I can solve this question :
Simplify (4 4cos^4 x)/(sin^2 x) and write in terms of sin x Answered by Penny Nom. 





siin (A) and sin (A/2) 
20130509 

From shanaia: given that sin A=4/5 and A is obtuse.find sin (A/2) Answered by Penny Nom. 





Find the height of the tower 
20130428 

From nombulelo: the shadow of a tower,when the angle of elevation of the sun is 30 degrees is found to be 40 meters longer than when it is 45 degrees. Find the height of the tower Answered by Penny Nom. 





A cone problem 
20130414 

From Courtney: Hello,
I am having difficulty solving this cone problem. The biggest challenge I have is figuring out what angle they are talking about:
The angle at the base of a cone is 34.5 degrees. Find the diameter of the cone at point on the edge of the cone 26cm from the tip. Answered by Penny Nom. 





A shortest distance problem 
20130328 

From LYNDELL: I have a right triangle and know the length of all sides. How do I calculate the shortest distance from the vertex of the 90 degree angle to the hypotenuse? Answered by Penny Nom. 





Trigonometry 
20130323 

From Tizoc: I am in a trig class and I have a conflict. When solving the length of a side, I know what trig function to use, but I do not know what angle to use in a calculator. To make this a little more understandable, if I have all the angles available in a right triangle and I use the tangent function, how do I know what to use?
Heres what I do not know what to put in my calculator: Tan(?)
Thanks in Advance! Answered by Penny Nom. 





Solve sin 3x = 0.1254 with x between o and 360 degrees 
20130221 

From David: sin 3x = 0.1254 0 Answered by Harley Weston. 





Solve sin 3x = 0.1254 with 0 
20130221 

From David: sin 3x = 0.1254 0 Answered by Harley Weston. 





A trig word problem 
20130218 

From Amy: Susan notices an unusual rock formation at an angle of 30 degrees to the right of her direction of travel as she is white water rafting. as she continues in a relatively straight path for 20 m, the rock formation appears to be at 45 degrees to the right. she cotninues until the rock formation is directly to her right. how far is she fromt he rock formation? Answered by Penny Nom. 





The height of an aerial 
20130212 

From ASIT: A vertical aerial stands on a horizontal ground. A surveyor positioned due east of the aerial measures the elevation of the Top as 48 degree. He moves due south 30metre and measure the elevation as 44 degree. determine the height of the aerial Answered by Penny Nom. 





The fourth side of an irregular polygon 
20130201 

From Emran: I have a irregular polygon. I know 3 of the 4 sides, and 2 of the angles. AB is 285, BC is 149, and CD is 310. Angle B is 135 degrees. and Angle C is 45 degrees. Is there a formula to solve for the final side? Thanks. Answered by Penny Nom. 





A boy walks 3km due east and 4km due north 
20130201 

From Kayode: Question from Kayode
A boy walks 3km due east and 4km due north. Find the bearing of the final point and the distance of the final position from the starting point. Answered by Harley Weston. 





Solve 2sin(2(theta))+sqrt(3)=0 
20130119 

From Kaitlyn: how do you solve 2sin(2(theta))+sqrt(3)=0 with the interval [0,2pi) Answered by Penny Nom. 





A shed roof 
20130112 

From christine: A roof on a shed is 7.3 ft wide has an incline of 20 degrees what is the height? Answered by Penny Nom. 





A trig identity 
20130104 

From Tehmas: Prove sinC+sinD=2sin(C+D/2)cos(CD/2) Answered by Harley Weston. 





The angles of elevation and depression 
20121203 

From Chelsey: a person on a balcony of one building looks towards a second building. if the angle of elevation to the top of the second building is 25 degrees, the angle of depression to the bottom of the second building is 17 degrees, and the balcony of the first building is 22 feet above the ground, what is the height of the second building? Answered by Penny Nom. 





Practical uses of trigonometry 
20121111 

From Michael: Where can I find books or information on real life function of sine and cosine? Answered by Penny Nom. 





The derivative of y = sin (30º + x) 
20121107 

From Saskia: derivative of y = sin (30º + x) Answered by Harley Weston. 





My compass was off by 8 degrees 
20121030 

From Oscar: If I walked 620' and my compass was off by 8 degrees how many feet from my heading was I?
Thank You Answered by Penny Nom. 





A label to cover a plastic cup 
20121023 

From Kevin: I'm trying to make a label to cover the entire outer area or a plastic cup. I know there must be a way to figure out the dimensions needed, but I can't seem to figure it out. The circumference of the bottom of the cup is 21.4cm and the circumference at the top of the cup is 29.8cm. The cup is 14.5cm tall. What should the height of the arc from the plane connecting the two ends of the 21.4cm arc. I attached a diagram where x is the value I'm looking for. I'm guessing there is some simple relationship between the length of a line and the arc needed to turn that line into a perfect circle, but I don't know what it is. Can you figure this out and share it with me? Thanks.
Kevin Answered by Penny Nom. 





A tank with an inner walled compartment 
20121012 

From don: I have a tank 20 feet diameter, 19' 8" tall with an inner walled compartment that has a 7' 6" radius arc with in the tank. I need to figure out the volume of the inner area and the volume of the larger area. Answered by Harley Weston. 





The height of a building 
20120908 

From Lin: How do surveyors determine a height of a building 150 feet away with an observation angle at 40 degrees?
What is the elevation of that top floor? Answered by Penny Nom. 





Making a wind sock 
20120828 

From John: I am trying to build a wind sock and need to be able to lay the shape
out on cloth. I need the wind sock front opening (diameter) to be
3 1/2" and the rear opening diameter to be 1". The windsock needs
to be 9 1/2" long. I tried using the example of the person trying to
make a crayfish trap but got confused and could not figure out my
numbers. Any help would be greatly appreciated.
Thanks
John Answered by Penny Nom. 





A tapestry rod on a curved wall 
20120814 

From Marlyn: I have a curved wall with a radius of 6'. I am trying to have a 36" rod made to hang a tapestry and need to figure out the degree measure of the arc.
Can you help me please? Answered by Penny Nom. 





The height of an isosceles triangle 
20120710 

From ken: I am trying to determine the various heights of an isosceles triangle, if each has the same base dimension and varies in the degree of the base (equal) angles. What is the method to do this?
As an example, of the base is 10, and the two equal angles are each 45 degrees, what is the height? With the same base (10), but with the two equal angles at 60 degrees, what is the height? And with the same base (10) and the two equal angles at 75 degrees, what would be the height?
I know how to calculate the degrees of the third angle (add the degrees of the known angles, and subtract from 180); but am unsure if that is needed for figuring the overall height.
And to be clear; I am not looking for the length of the sides of the triangle, but the height from the base to the top point.
Thank you! Answered by Chris Fisher. 





A 10 inch circle using 2x4s 
20120519 

From Ralph: I want to form a 10" circle with 4"high pieces of 2 x4's. If each 2x4 piece sit next to each other,What degree would I have to cut
each side of the 2x4's, and how many would I need to form a 10 inch circle. I know there is a formula for this out there somewhere. Answered by Harley Weston. 





Two golf drives 
20120514 

From peter: If a golf drive travels 250 yards with a perfectly perpendicular hit,
what is the length of the base, if a second golf drive is off line
by one degree? Answered by Penny Nom. 





cos(theta/30) = 1 
20120514 

From Hope: cos (theta / 30 = 1
I am very confused as to how to solve it. Can you help? Answered by Penny Nom. 





The derivative of 2sin cubed x  3 sin x 
20120325 

From holly: suppose f(x) = 2sin cubed x  3 sin x
show that f 1(x) = 3 cos x cos 2x Answered by Harley Weston. 





Angle measures 
20120321 

From jogiboy: how can i get the sine theta if the given is 3.14/3 Answered by Penny Nom. 





Tangent of theta 
20120117 

From stahl: explain what the 'tangent of theta' means. Draw and label a diagram to help with your explanation. Answered by Harley Weston. 





A circle inscribed in a regular octagon 
20120116 

From Eric: I have a circle inscribed in a regular octagon. How do I determine the length of one side of the octagon if I know the radius of the circle (2.75 inches) ? Answered by p. 





The radius of a circle 
20120112 

From Janie: Find the radius of a circle knowing that a chord of 24.6 inches has a corresponding arc of 70°. Answered by Penny Nom. 





A trig identity 
20120108 

From Joe: Prove this Trig. Identity :
((cos2θ + sinθ1) / tanθ ) + sin2θ = cosθ Answered by Penny Nom. 





The height of a tower 
20120106 

From trevor: A tower is on the top of a hill. It is 2,400 feet from an observer to a point directly under the tower and at the same elevation as the observer. The angle of elevation from the observer to the base of the tower is 15 degrees and to the top of the tower 23 degrees. How tall is the tower in feet? Compute your answer within one foot. Answered by Penny Nom. 





The height of a flagpole 
20111207 

From Grail: at a certain point the angle of elevation of the top of a flagpole which stands on a level ground is 35 degree. 75 ft. nearer the pole, the angle of elevation is 50 degree. How high is the pole Answered by Penny Nom. 





What is the altitude of the balloon? 
20111204 

From C: Chelcy and Jorgeare 2.32 miles apart. The observe a hot air balloon directly overhead between them Chelcy's angle of elevation is 28 degrees. Jorge's Angle of elevation is 37 degrees. What is the altitude of the balloon? Answered by Penny Nom. 





Solve for theta if 8cos^2 theta3=1 
20111202 

From Katherine: Hi,
I have just learned to solve trigonometric problems for theta and have one specific question in order to find the solutions to my homework.
I will use one example for this question. If I have 8cos^2 theta3=1
I first divide by 8 and get cos^2theta=3/8
then I have cos theta= plus or minus the square root of 3/8
Then I assume that I plug in inverse cos (the square root of 3/8) to my calculator.
How do I find the four solutions (we are typically supposed to find four, I believe?)
Can you help me with finding the solution to this problem? Thank you! Answered by Penny Nom. 





The height of a flag pole 
20111121 

From Micah: A flagpole stands vertically at the edge of a roof of a building 200 ft high. the angle of elevation of the pole from a point 100 ft from the bottom of the building is 67 degrees. Find the length of the pole in meters. Answered by Penny Nom. 





sin A/1+cos A + 1+cos A/sin A = 2cosec A 
20111020 

From Neeraj: sin A/1+cos A + 1+cos A/sin A = 2cosec A Answered by Penny Nom. 





The height of a building 
20110909 

From Sally: A building's angle of elevation from a point on the ground 60 ft. from its base is 32 degrees. What is the height of the building? Answered by Penny Nom. 





Find the distance from the ladder's base to the wall 
20110819 

From Donna: A 16 foot ladder leans against a wall at a 67 angle of elevation I need to find the distance from the ladder's base to the wall Answered by Penny Nom. 





A stained glass lamp 
20110725 

From Guy: Like Kay, I also work in stained glass, but in 3dimensions. I am
frequently asked to replicate lamp shades in stained glass where the
diameter of the top is different (narrower) from the diameter of the
bottom (which is wider). Some people want 5, 6, 7, 8, 10, 12, 16, ,,,
nsided shades. Is there a formula I can use to determine the width
of the sides using the angle, if I remember correctly, I think it's
called theta. In other words, is there a formula where I can plug
in the angle which describes the arc of the circle. For instance, if
someone asks for a 7 sided shade, plugging in 51.43 (360/7). I
could then use that to determine the width at the top and bottom
rings to create the appropriate trapezoids. I've visited a few sites
so the formula looks like its a function of sin & cos but they are
presented like proofs for teaching. Your site appears to want to
actually answer questions without making the inquirer feel stupid. Answered by Harley Weston. 





The length of a belt around three pulleys 
20110518 

From Grant: I need to calculate the belt length around these pulleys, please can you
help or refer me?
Known variables
D  Large Pulley Diameter
d  Small Pulley Diameter
c  Center Distance between D and d
T  Tension Pulley Diameter
x  Horizontal Distance between T and d' Centers
y  Vertical Distance between T and d's Centers
I need to calculate the belt length around these pulleys.
Kind Regards,
Grant Answered by Harley Weston. 





cos(x) = 1/(square root of 2) 
20110427 

From Shelby: Find exact value of x for 1 <(or equal to) x < 2pi
a) cos(x) = 1/(square root of 2) Answered by Penny Nom. 





Two trig equations 
20110420 

From Tony: find the value of pi in the following:
sin pi= cos(pi + 40)
sin(80  pi)=cos pi Answered by Penny Nom. 





1 = sin^2x  cos^2x 
20110411 

From veronica: I need the solutions for 1 = sin^2x  cos^2x Answered by Penny Nom. 





Reallife applications of trigonometry 
20110410 

From Angela: I am a teacher and I desire to show the students the reallife
application of trigonometry.
Of course, one application is to use a clinometer and find the heights of
various things. However, I am trying to provide a reallife scenario
which also answers the question "why" the height of the object needs
to be found. Not being an engineer, I do not know the specifics
examples, but I want my information to be accurate and my example to
to be as reallife as possible. I mean, I can say that someone wants to know the height of a flagpole;
however, I also want to answer the question "why" they want to know
this. I would like to give an actual reallife scenario. Do you know of some?
Thanks! Answered by Penny Nom. 





sin x = 0.25 
20110329 

From Wayne: How do you solve for x in the equation sin x = 0.25
the answer is 3.394 and 6.030 but I don't know the steps they used to calculate this Answered by Penny Nom. 





A true or false trig question 
20110324 

From Abeth: True or False: Since cot (theta) = cos (theta)/sin (theta), if cot (theta) = 1/2, then cos (theta) =1 and sin (theta)=2.
My answer before was true, but not my answer is false. Can you give me a solution on this matter. thanks. Answered by Penny Nom. 





Prove sin x = sin (pi  x) 
20110215 

From Janet: Prove sin x = sin (pi  x) Answered by Penny Nom. 





A fence around a water tank 
20110201 

From Heath: I am building a fence around a water tank. the fence is to be in the shape of a normal octagon. The tank has a circumference of 57 ' 6''. I would like the fence to be 3 ft from the tank at the skinny point . How would I calculate(for the simple guy) where to set each of my 4x4 posts at the 8 corners. Any help would be greatly appreciated. Answered by Harley Weston. 





tanθ=1.192 
20110115 

From Adori: Use a calculator to approximate two values of the θ (0 ≤θ≤2π) that satisfy the equation.
a) tanθ=1.192
I do not understand how to find the second value of θ. Answered by Harley Weston. 





Tan(x+pi)tan(pix)=2tan(x). 
20110109 

From Steven: Verify the identity:
Tan(x+pi)tan(pix)=2tan(x) Answered by Penny Nom. 





[sec^2x]*[sec^2x] 
20101216 

From Hari: [sec^2x]*[sec^2x]=...? Answered by Penny Nom. 





How far must the pitcher travel to get to the ball? 
20101104 

From ken: A baseball player bunts a ball down the first base line. It rolls 35ft at an angle of 26 degrees with the first base path. The pitchers mound is 60.5 ft from the plate. How far must he travel to get to the ball. Answered by Penny Nom. 





A problem that can be solved using trigonometry and geometry 
20101029 

From xolani: In your neighbourhood find a problem that can be solved using trigonometry and geometry. write a report on the problem and how you solved it. the report should contain:
a) a clear description of the problem, accompanied by a diagram and all necessary measurements.
b) a solution to thje problem, showing all calculations.
c) proper theorems and rules must be used as part of the solution. Answered by Robert Dawson. 





sin14.5/a = sin150/280 
20101026 

From ken: how do you do the steps to this equation. sin14.5/a = sin150/280 the text book answer is 140.21 miles ,but how do the steps? Answered by Penny Nom. 





A building and a flag pole 
20100909 

From paul: A flag pole and a building stand on the same horizontal level. From the point p at the bottom of the building,the angle of elevation of the top t of the flag pole is 65 degrees. From the top q of the building the angle of elevation of the point t is 25 degrees.If the building is20 meters high. Calculate the distance pt Answered by Penny Nom. 





The shadow of a building 
20100728 

From vera: building casts a shadow 210 ft. long,40 degree angle.How tall is the building? Answered by Penny Nom. 





An octagon shaped bench 
20100709 

From rob: i am trying to build a octagon shaped bench to fit inside a 69 inch round hot tub so that the tip of each point touches the edge of the circle where it will be fastened. Answered by Stephen La Rocque. 





The capilano suspension bridge 
20100603 

From nida: the capilano suspension bridge in north vancouver is the world's highest footbridge of its kind. the bridge is 140m long . from the ends of the bridge the angles of depression of a point on the river under the bridge are 41 degrees and 48 degrees. how high is the bridge above the river to the nearest metre Answered by Penny Nom. 





Integration of sin^3 (2x) 
20100529 

From ascher: how do you integrate this equation
∫ sin^3 (2x) dx Answered by Robert Dawson and Penny Nom. 





The altitude of a triangle 
20100508 

From kylie: the vertex angle of an isosceles triangle is 57 degrees 24 minutes and each of its equal sides is 375.5 feet long. find the altitude of the triangle Answered by Penny Nom. 





A trig equation 
20100428 

From Steve: 2cos^2(X)2sin^2(x)+1=0 Answered by Harley Weston. 





cos(x) = sin(x  1) 
20100428 

From alex: In the equation cos x = sin x1 for pi/2
A: solve for x graphically
B: solve algebraically and prove the solution is correct.
Alex Answered by Penny Nom. 





The height of a flag shaft 
20100425 

From Sarah: A man standing 20metres away from a tower observes the angles of elevation to the top and bottom of a flag shaft standing on the tower as 62degrees and 60degrees respectively. Calculate the height of the flag shaft.' Answered by Penny Nom. 





Solving a trig equation 
20100421 

From Jason: Please Help! My question is :
Find all of the solutions to sin(x/2)+cosx1=0 Answered by Penny Nom. 





Polar coordinates 
20100414 

From Lan: Given the rectangular equation (x^2)+2x+(y^2)+y=0, find the polar equation. Answered by Harley Weston. 





Vapor trails 
20100412 

From Frank: I'm not sure if this is a proper question to ask so if I have misdirected my question I apologize and no response is expected. I am trying to figure out a way to measure vapor trails from my back yard in Phoenix Arizona. If I used a compass and spread each point of the compass to the start and finish of the vapor trail I would have the angle of an isosceles triangle. The other two angles would be identical. The height of from the inverted base of the triangle to my standing spot on the ground would be about 35,000 feet. I'm thinking that there should be a way to figure out the length of the inverted base (vapor trail) but I'm devoid of mathematical skills and can't seem to figure out how to do this. Is it possible to figure out the length of a vapor trail using this method or do you have an easier way to accomplish the task?
Any help you could offer would be most appreciated.
Thanks....Frank Answered by Harley Weston. 





A trig identity 
20100327 

From Anne: Prove:
(2tanxsin2x)/2sin^2x=tanx Answered by Penny Nom. 





The height of a hill 
20100326 

From Amber: A surveying team determines the height of a hill by placing a 12foot pole at the top
of the hill and measuring the angles of elevation to the bottom and to the top of the pole.
They find the angels of elevation. Describe how to find the height of the hill. Answered by Penny Nom. 





A radio tower 
20100326 

From Alex: The height of a radio tower is 450 feet, and the ground on one side of the tower slopes upward at an angle of 10 degrees. How long should a guy wire be if it is to connect to the top of the tower and be secured at a point on the sloped side 110 feet from the base of the tower? Answered by Harley Weston. 





A 6m ladder is placed against a wall 
20100309 

From Trevor: A 6m ladder is placed against a wall making a 56 degree angle with the ground. How far up the wall does the ladder reach? Answered by Harley Weston. 





A trig identity 
20100308 

From Kim: I am having trouble proving this trig identity
(sin^2 x + 2 cos x1) / 2+cos x  cos^2 x = 1/ (1+ sec x) Answered by Penny Nom. 





The integral of X^3/the square root of 1x^2 dx 
20100307 

From William: The integral of X^3/the square root of 1x^2 dx. Answered by Harley Weston. 





The other two sides of a right angle triangle 
20100209 

From ayesha: how to find the other two sides of right angle triangle when length of one side and angle of other side is given i.e 45 Answered by Penny Nom. 





The height of a roof 
20100131 

From carl: Width of my roof I am building is 5M at baseline, and the pitch is 40%.
What will the height be, and how can I work this out in the future. Answered by Penny Nom. 





A trig identity 
20100124 

From Natalie: hi, i need help proving the following trig identity. i cant seem to figure out how to do it.
thanks so much.
(1+sin2x)/cos2x = cos2x/(1sin2x) Answered by Penny Nom. 





A trig problem 
20100122 

From vinton: ok there is a triangle labled q, p, r......the three towns p, q, r are such that the bearing of p from q is 070 degrees.
r is 10 km due east of q and pq = 5km.
(i) calculate correct to one decimal place, the distance of pr.
(ii) given that angle qpr 142 degrees, state the bearing of r from p Answered by Penny Nom. 





A trigonometric equation 
20100121 

From Laura: Find the exact solution for sin4t + √3sin4t = 0 for t when (o ≤ t ≤ π Answered by Harley Weston. 





A trig identity 
20100121 

From Alesia: How to prove Csc(A+B) = (csc A Csc B)/ (Cot A+ Cot B) Answered by Penny Nom. 





How far apart are the two girls? 
20100118 

From benny: Debby and john are looking up at their house from the backyard. From Debby's
point of view, the top of the house is at an angle of elevation of 40 degrees
From Johns point of view, directly closer to the house, it is 60 degrees. The
house is 15m high. How far apart are the two girls? Answered by Robert Dawson. 





Trigonometry and picture hanging 
20100113 

From george: The top of a picture 1m high 0.8m from the ceiling. At a point on the ceiling directly in front of the picture, we wish to install a light so that the angle subtended by the picture equals to the angle of depression of the top of the picture. How far out from the wall should the light be installed? Answered by Penny Nom. 





A trig identity 
20100105 

From Christine: I need help with this whole paper here is one problem
csc^2xcot^2x/1sin^2x=sec^2x
by the ^2 i mean squared pleease Answered by Penny Nom. 





tan x= cos 100 
20100104 

From Ruby: Given that tan x= cos 100 and x=0180. calculate the value of x. (All measurements in degrees) Answered by Robert Dawson. 





The height of a mountain 
20100102 

From Aye: In order to decide the height of a remote mountain peak T one measures from two points A and B the angles u and v where the lines AT and BT made with the Horizontal plane respectively. From B, which lies 2400 m from A, one can see A and T by the same point of the compass. Find the height of a mountain peak, if A and B are known to be 950 m and 875 m above sea level respectively, as well as u = 43,8 degree and v = 25,2 degree.
Aye Answered by Harley Weston. 





A trig question 
20091215 

From A trig question: Hey, my name is Candle
I'm in academic math10 and am stuck on my trig... one question I thought I had right because i used the cosine law I got wrong and can't figure out why... here's a copy of the question. (i guessed it was D... but my teacher said it's B)
Thanks
Candle Answered by Robert Dawson. 





A telephone pole on a slope 
20091214 

From Marissa: A 10 meter telephone pole casts a 17 meter shadow directly down a slope when the angle of elevation of the sun is 42 degrees. Find the angle of elevation of the ground. Its a law of sines problem. Answered by Penny Nom. 





f(x)=x+2sinx 
20091212 

From amroziz: for which values of x does the graph of f(x)=x+2sinx have horizontal tangent Answered by Harley Weston. 





The height of an isosceles triangle 
20091206 

From Carl: What is the height of an isosceles triangle if its base is 12cm, and its base angle is 72degrees? Answered by Penny Nom. 





sin x / 1+ cos x = csc x  cot x 
20091118 

From Mansi: i need a hint on how i could prove the following identity:
sin x / 1+ cos x = csc x  cot x Answered by Harley Weston. 





A truncated cone 
20091111 

From Lucian: I need to calculate the bottom inside diameter of a truncated cone.
The top insdie diameter is 1450mm.
The material is 6mm thick
The cone angle is 20 degrees
The slant length is 152mm
I would like a formula so that I can build a spread sheet Answered by Penny Nom. 





y = sin(x) + 3 
20091110 

From Kapilan: When graphing trigonometric functions like SIN and COSINE does f(x)=x
squared equal to SIN or COSINE
Also what is the range, domain, period and ampliltude for y=sin@ + 3 Answered by Harley Weston. 





sinA + cosA = 1 
20091106 

From Nazrul: What is the solution of sinA+cosA=1 where A is an acute angle? Will A=0 degree be included in the solution? Please explain. Answered by Harley Weston. 





A minute hand 
20091105 

From Pardha: A minute hand of table clock is 3cms long. How far its tip move in 20 minutes Answered by Penny Nom. 





Cutting a pipe at an arbitrary angle 
20091024 

From Carol: I have read your article on cutting pipe,etc. at a 45 degree angle. I need to develop
an equation and pattern for cutting any size pipe (3" to 7") to any degree. I don't
understand how to transfer the wave pattern to graph paper.
Thanks. Answered by Harley Weston. 





Find the intersection of y=x1 and y=sin(x) 
20091010 

From Usama: There are many modern calculators and softwares that can plot the functions.
I have two very simple equations y=x1 and y=sin(x), if i draw them manually on paper i can not get the accurate value.
But i think a computer can easily draw perfect straight and curve lines so it should be easy to find the intersection point of two lines.
Is there any way or software that can tell the exact value of intersection point of two lines? Answered by Robert Dawson and Harley Weston. 





How high is the ledge? 
20091003 

From gabby: Standing on a ledge, there is a boat 25 degrees below you. The boat has a 1,000ft. tower. If the angle of elevation to the top of the tower is 15 degrees, how high is the ledge? Answered by Stephen La Rocque. 





Hexadecagon 
20090920 

From Rick: Is there an easy way to figure the even side lengths of a Hexadecagon in layman's
terms, so I know how long to cut the exterior support boards for my pool deck.
The pool is a 16' diameter Hexadecagon and my Wife wants a 4' wide splash deck
all the way around which would make the outside 24' in diameter. Answered by Chris Fisher and Harley Weston. 





How deep is the hole? 
20090825 

From Scott: If I have a hole three foot in circumference that runs at a 15degree angle from the surface and continues for a length of 100 feet, how deep would the hole be at 100 feet? Answered by Penny Nom. 





The leaning tower of Pisa 
20090809 

From MF: Would you have any idea how the 'latitude of 44 degrees N" has anything to do with this question and how I would apply it?
The leaning tower of Pisa leans toward the south at an angle of 5.5 degrees. One day near noon its shadow was measured to be 84.02 m long and the angle of elevation from the tip of the shadow to the top of the tower was measured as 32.0 degrees. To answer the question, assume that the tower is like a pole stuck in the ground, it has negligible width. Also, it is important to know that Pisa Italy is at a latitude of approx 44 degrees North because this affects the direction of the shadow.) Answered by Stephen La Rocque. 





sinAcosA=1 
20090730 

From Nazrul: How can I solve sinAcosA=1 where 0 degree<=A<=90 degree. Thank you. Answered by Harley Weston. 





A trig identity 
20090710 

From sam: I need to prove:
tan x (cot x + tan x) = sec2 x
(the "sec2" is "sec squared")
I am totally stuck!!
Thanks! Answered by Stephen La Rocque and Harley Weston. 





A trig identity 
20090630 

From sumayya: prove that sin A (1+tan A)+cos A (1+cot A)= sec A+ cosec A Answered by Robert Dawson. 





Finding an Acute Angle using Trigonometric Identities 
20090629 

From Nazrul: How can I find the value of A if sinAcosA=1 , where A is an acute angle. Answered by Stephen La Rocque. 





Ground Velocity of an Aircraft 
20090607 

From Anna: An aircraft is flying at 180km/hr and there is a northerly wind of 35km/hr. The pilot steers the aircraft at an angle of 40 degree east of north. Which direction (in degrees east of north) is the aircraft travelling over the ground? Answered by Stephen La Rocque. 





How long are the rafters? 
20090603 

From Tina: An architect designs a house that is 12 m wide. The rafters holding up the roof are equal in length and meet at an angle of 70 degrees. The rafters extend 0.3 m beyond the supporting wall. How long are the rafters? Answered by Penny Nom. 





sin x/ 1+cos x = 1cos x/ sin x 
20090530 

From rita: prove: sin x/ 1+cos x = 1cos x/ sin x Answered by Stephen La Rocque. 





Two ships and a lighthouse 
20090527 

From Chelsey: I have a question in regards to how do I know when to use tangent or cosine when determining angles. The question is: Looking north from the observation deck of a lighthouse 60 m above the sea, a lighthouse keeper sees two ships. The angles of depression to the ships is 5 degrees and 10 degrees. How far apart are the ships?
I don't understand which one to use when solving the equation. Answered by Harley Weston. 





sin54 cos36/cos18  2cos36 2sin18 = ... 
20090523 

From citra: sin54 cos36/cos18  2cos36 2sin18 = ...
thank you very much.. Answered by Stephen La Rocque. 





Application of Derivatives of Trig Functions 
20090521 

From Alannah: I have a word problem from my Calculus textbook that I can't figure out.
Triangle ABC is inscribed in a semicircle with diameter BC=10cm. Find the value of angle B that produces the triangle of maximum area.
I am supposed to set up an equation for the area of the triangle A=b x h/2 using Trig functions based on angle B to represent the base and height but I'm not sure how to do this when the side length given is not the hypotenuse. Answered by Janice Cotcher. 





4cos^2 (3x) + 3sin (3x) = 1 
20090505 

From Cheryl: Find all solutions of the following equation and show how to do this algebraically.
4cos^2 (3x) + 3sin (3x) = 1 Answered by Harley Weston. 





Practical trigonometry 
20090504 

From Lori: I am an exmath major turned homeschooling parent. I would desperately like to find a wordproblem based trigonometry book for my 17year old son. I don't want graphing or other gobbledygook that he'll never use. Does such a thing exist? Answered by Robert Dawson. 





A two goat problem 
20090427 

From Michael: if you have a goat tied to a pole at one corner of a square paddock with one length of a side being 24m.
what length must the rope be for the goat tied up to graze half the paddock?
and if another goat is placed on the opposite corner and same length what is the amount of area they share grazing ? Answered by Stephen La Rocque and Penny Nom. 





(1+2sinxcosx)/(sinx+cosx) = sinx+cosx 
20090423 

From Katie: Solve this identity: (1+2sinxcosx)/(sinx+cosx) = sinx+cosx
Thank you ! Answered by Stephen La Rocque. 





A vertical radio tower is located on the top of a hill 
20090421 

From Rafael: A vertical radio tower is located on the top of a hill that has an angle of elevation of 10 degrees. A 70foot guy wire is attached to the tower 45 feet above the hill.
a. Make a drawing to illustrate the situation
b. What angle does the guy wire make with the side of the hill?
c. How far from the base of the tower is the guy wire anchored to the hill?
What confuses me about this problem is the visual situation. Isn't the angle of the guy wire with the side of the hill the same as the angle of elevation? And if not, then how is one supposed to find the other angles without any more information? Answered by Harley Weston. 





cos2x = sinx 
20090419 

From stacey: solve the equation cos2x = sinx for 0 < x < 2 pi
giving the answer in terms of pi. Answered by Harley Weston. 





2sinB=3tanA 
20090410 

From Xanathax: ABC is a rightangled triangle. 2sinB=3tanA.
Calculate the measure of angle A. Answered by Penny Nom. 





A ladder against a wall 
20090408 

From Jessica: The angle of elevation of a 15 ft. ladder is 70 degrees, find out how far the base of the ladder if from the wall. Answered by Penny Nom. 





The perimeter of a pentagon 
20090407 

From Malysa: A pentagon has an area of 1400 cm squared. Determine its perimeter. Answered by Harley Weston. 





An arched or round top window 
20090407 

From Dale: I need a formula to figure the lineal footage of trim require to trim an arched or round top window. The variables that I have consist of the width of the window the height of the arc and the radius. Answered by Harley Weston. 





2sin^2xsinx=0 
20090402 

From Jose: 2sin^2xsinx=0
and i know the answer
im just having trouble figuring out how it went from the original equation to sin(x)2sin(x)1=0? Answered by Harley Weston. 





The height of a mountain peak 
20090323 

From james: Can you please help us (my son Jim geometry) out with this problem, we
cannot seem to find the correct method of solving, not sure how to solve the
scalene triangle with what is given...if that's the correct method?? Can you
please explain how this is solved!!
Thank you so much,
Jim and son ! Answered by Harley Weston. 





An impossible trig problem 
20090314 

From Alisha: If csc theta = 3 and sec theta = square root of 3, what are the values of tan theta and cos^2 theta? Answered by Harley Weston. 





sin x + cos x = x 
20090306 

From Ashley: For what values of x is the following true:
sin x + cos x = x Answered by Robert Dawson. 





For what x is cos x is greater than root 3 over 2? 
20090225 

From Robert: cos x is greater than root 3 over 2
Restrictions: between 0 and 2pi Answered by Harley Weston. 





cos 2x = 2 sin x 
20090225 

From Bobby: cos 2x = 2 sin x Answered by Harley Weston. 





Trig functions without geometric data 
20090224 

From bob: I do not understand how it is possible to find the sine, cosine, or tangent of an angle if
there is no hypotenuse, opposite or adjacent side?! Answered by Robert Dawson. 





Find all values of 2sin4x + (Sqrt)3 = 0, in [0, 2pi] 
20090221 

From Sam: Find all values of 2sin4x + (Sqrt)3 = 0, in [0, 2pi]. Answered by Harley Weston. 





Angle of depression 
20090218 

From Meeka: An aircraft flying at an altitude of 2000m is approaching an airport.
If the angle of depression of the airport is 5 degrees, what is the distance from the plane to the airport measured along the ground?
Round your answer to the nearest tenth of a kilometer. Answered by Robert Dawson. 





A trig limit 
20090205 

From Samantha: lim x> 0 ( ( r*cos(wt +h) + r*cos(wt) )/ h )
Where r & w are constants. Answered by Harley Weston. 





A trig limit 
20090205 

From Kathy: Hi! I was just wondering how to do this question:
lim 1cos2x/xsinx as x approaches 0
Thanks,
Kathy Answered by Penny Nom. 





The grade of a roadway 
20090126 

From black: A highway that has a 6% grade rises 6 ft vertically for every 100 ft horizontally. Which trigonometric ratio is being used in reporting the 6% grade? Explain why Answered by Stephen La Rocque. 





A trig problem 
20090118 

From Conor: sinx= 6/10 ; Find the exact value of cos(squared) x / 1tanx Answered by Harley Weston. 





A applied math trig problem 
20090113 

From Simon: I wish to find all the answers for the following equation over the interval (0,1):
cos^2(pi * n^x) + cos^2(pi * n^(1x))  2 = 0
where n is any integer > 0 Answered by Robert Dawson and Harley Weston. 





Trig identities 
20090105 

From Michael: 1) Determine if the following is an identity. If it is, prove it, If it isn't state it.
tan x + cot x = sec x * csc x
and
1  (cos^2) x = 1+ (cot^2) x Answered by Robert Dawson and Harley Weston. 





Pouring angles for a crucible 
20081220 

From Richard: I am trying to work at pouring angles and volume left in during pouring a crucible, The crucible is cylindrical and flat bottomed.
I know the diameter, radius and volume of the crucibles. and the volume of liquid going into it.
So lets say the crucible is only half full firstly I need to work out the angle just before its going to pour. ( I can work this out as long as there is a certain volume of liquid if its not enough I cant do it)
Now the problem I also need to work out how much I should tilt the crucible to allow a certain amount out and be able to do this untill the volume reaches 0 at 90' turn. This is where I am stuck.
The reason for needing to be able to work this out is so i can develop a constant flow for example 10Kg of metal per second.
Thank you very much for you time Answered by Harley Weston. 





Limit of a Trig Function 
20081206 

From Berta: Evaluate limit xcsc2x/cos 5x as x goes to 0
ans is 2 but I get 1/2
x/sin2xcos5x = 2x/2sin2xcos5x= 1/2cos5x Answered by Penny Nom. 





How high is the flagpole? 
20081202 

From michael: 100 m from the base of a flagpole the angle of elevation of the top of the flagpole
is 7degree 16'12".how high is the flagpole Answered by Harley Weston. 





A trig identity 
20081125 

From Jeff: i cannot prove this trigonometric identity. please help!
(cos x)^3 – (sin x)^3 = (cos x –sin x) (1+cosxsinx) Answered by Chris Fisher. 





Sec(2x) 
20081123 

From Evan: Prove that this is an identity...
sec2x = sec^2x / 2  sec^2x Answered by Harley Weston. 





How far are the boats apart? 
20081114 

From dom: Two boats leave port at the same time. They leave at 150 degree angle. One boat travels at 10mph and the other at 20mph. After two hours how far are the boats apart? Answered by Penny Nom. 





A trig Identity 
20081113 

From Rebecca: Question from Rebecca, a student:
How do I prove:
1/sin@ csc@ 2sin@
________ + ______ = _____
1 + CSC@ 11/sin@ cos^@ Answered by Penny Nom. 





A barrel on its side 
20081113 

From Dave: Question from Dave:
How many gallons are left in a 36x60 in. barrel (laying on its side) and has 16 in. of gasoline left. I have attached a diagram. Answered by Harley Weston. 





A trig limit 
20081104 

From Teri: Although I have this problem completely worked out in front of me I still cannot understand
how it was done. The problem is:
Find the limit.
lim x>0 sin2x/tan7x. Answered by Harley Weston. 





A trig identity 
20081103 

From Student: verify cos(2x)=(cot(x)tan(x))/(cot(x)+tan(x)) Answered by Penny Nom. 





Sin(theta) = 3 
20081024 

From jonathan: how can i solve this if the only given is sin theta= 3
tan theta=
cos theta=
cot theta=
co secant theta=
secant theta=
can you teach me and show how to solve?? Answered by Stephen La Rocque. 





cos^2x  3cosx = 1 
20080929 

From Danielle: cos2x  3cosx = 1 Answered by Penny Nom. 





How tall is the wall? 
20080929 

From ash: you and bob are separated by a tall wall you stand 10 feet further from the wall
than bob your angle of elevation is 37 degrees and his 44 degrees
how tall is the wall? Answered by Penny Nom. 





Geometry with A Ladder Using Trig Functions 
20080920 

From Please: A ladder makes an angle of 50 degrees with the ground. if the base of the ladder is 10 feet from the building, how high up the building does the ladder reach?
i saw that someone else had a similar question, but we arn't using the pythagorean therom. we are using trig functions. Most of the problems we are doing is with the tangent. so this one probably is too. Answered by Penny Nom. 





Cutting a pipe at an arbitrary angle 
20080920 

From John: from the original question Al asked about cutting a 200 diameter pipe in 45 degrees. can someone explain the math steps required to creating the graph. I am trying to do the same thing only using a 150 degree cut. Answered by Harley Weston. 





Cutting a pipe on a 45 degree angle 
20080912 

From Bakshani: how do you a mark a pipe 5 inch diameter and cut it to form a 45 degree angel Answered by Stephen La Rocque. 





Angle of elevation 
20080909 

From kristy: A man on the tenth floor of a building shouts down to a person on the street. If the angle of elevation from the street to the man in the building is 35° and the man in the building is 40 feet up, about how far away from the building is the person on the street? Answered by Penny Nom. 





The height of a tree 
20080909 

From danice: At a certain time of day, the angle of elevation of the sun is 30°. A tree has a shadow that is 25 feet long. Find the height of the tree to the nearest foot. Answered by Penny Nom. 





Finding the Speed of a Truck 
20080908 

From Rita: A state trooper is hidden 30 feet from a highway. One second after a truck passes, the angle theta between the highway and the line of observation from the patrol car to the truck is measured.
(a) If the angle measures 15 degrees, how fast is the truck traveling? Express the answer in feet per second and miles per hour. Answered by Janice Cotcher. 





How far was the ship from the tower at 1:30 p.m? 
20080907 

From sam: A passenger on a ship sailing north at 5.0 mph noticed that at noon a radio tower on land was due east of the ship. At 1:30 p.m., the bearing of the tower from the ship was S35degreesE. How far was the ship from the tower at 1:30 p.m. Answered by Stephen La Rocque. 





A surveillance satellite 
20080904 

From Rita: A surveillance satellite circles Earth at a height of h miles above the surface. Suppose that d is the distance, in miles, on the surface of Earth that can be observed from the satellite.
(a) Find an equation that relates the central angle theta to the height h.
(b) Find an equation that relates the observable distance d and theta.
(c) Find an equation that relates d and h. Answered by Penny Nom. 





A 306090 triangle 
20080820 

From ronie: finding the sin,tan,sec,cos and csc.given is square root of 3 over 2.the question are how to find that? Answered by Penny Nom. 





Solving for Shared Height of Two Right Triangles 
20080817 

From Heidi: find the height of a triangle, which can be split into two right triangles, but the base (50m) is not split equally in half. one end of the base is 40 degrees, while the other is 30 degrees. Answered by Janice Cotcher. 





TRIG IDENTITIES 
20080817 

From VINCE: HOW DO YOU SIMPLIFY THE FOLLOWING:
2sin3(theta)cos3(theta)?
Regards Answered by Harley Weston. 





Finding Angles in a Pyramid 
20080730 

From Carla: A pyramid has its vertex directly above the centre of its square base. The edges of the base
are each 8cm, and the vertical height is 10cm. Find the angle between the slant face and the base,
and the angle between the slant edge and the base. Answered by Janice Cotcher. 





Trigonometric 
20080728 

From kiran: In triangle , Sin@ = ? Answered by Penny Nom. 





A trig problem 
20080727 

From Carla: PQRS is a rectangle. A semicircle drawn with PQ as diameter cuts RS at A and B.
The length PQ is 10cm, and angle BQP is 30deg. Calculate the length PS. Answered by Stephen La Rocque. 





How many gallons of fuel still in the barrel? 
20080722 

From Charles: I have barrel 6 feet long and 3 feet diameter that is laying on it's side with 5 inches of fuel, how many gallons of fuel still in barrel Answered by Penny Nom. 





Graphing Using Double Angle Identities 
20080716 

From Hodan: the Question is:
Describe how you could use your knowledge of Double angle formulas to sketch the graph of each function. Include a sketch with your description.A) F(x)=sin x cos x
B)F(x)=2 cos(squared)x
C) F(x)= tan(x) (divided) by 1tan(squared) x Answered by Janice Cotcher. 





A trig exercise 
20080714 

From Carter: let cos B = a, find cos 2B and sin 2B in terms of a and hence confirm that
cos^2 (2B) + sin^2 (2B) = 1 Answered by Harley Weston. 





Domain & Range of a Periodic Function 
20080711 

From Michelle: The depth, w metres, of water in a lake can be modelled by the function,
w=5sin(31.5n+63) +12 where n is the number of months since
January 1, 1995. Identify and explain the restrictions on the domain and
range of this function. Answered by Janice Cotcher. 





How far is the ladder from the wall? 
20080710 

From Al: a ladder is leaning against a wall at a 70 degree angle and the ladder is 20 feet tall...how far away is the ladder from the wall Answered by Penny Nom. 





Trigonometric equations 
20080709 

From Carla: Hello, my problem is as follows:
Solve the given equation for A, giving your answers in the interval from 180 to 180
4 sin A cos A + 1 = 2 (sin A + cosA) Answered by Harley Weston. 





sin(2x)/sin(3x) 
20080619 

From matt: how does sin2x break down (not with identities) and how would sin3x be created. My
prob. is sin 2x/ sin 3x and I want to know how the double(or triple angle) would break
down. I want to be able to cancel out sins. Thanks! Answered by Harley Weston. 





tan(4a  b) 
20080612 

From A student: hi guys just a quick help on question needed thanx
if tan a = 1/5 and
tan b = 1/239
find value of tan(4ab)
thanks alot in advance Answered by Harley Weston. 





The xintercepts of f(x)= 5sin (4x+pi/4) 
20080603 

From Tom: Hi, how would I find where the x intercept in this function f(x)= 5sin (4x+pi/4)? Answered by Janice Cotcher and Harley Weston. 





Applications of trigonometry 
20080524 

From Mohita: I have got a project in the school and i am not getting anything about the topic. The topic is that we need to find the application of trigonometry on any one of the real life situations using 3dimensional figures. I mean how can trigonometry can be used in real life situations like navigation, architecture, survey, astronomy etc. Answered by Penny Nom. 





sinx+cos(x+30degrees)=0 
20080517 

From geeta: sinx+cos(x+30degrees)=0 Answered by Stephen La Rocque. 





cos3A=1/3 find cos6A 
20080515 

From mike: cos3A=1/3 find cos6A Answered by Penny Nom. 





sin105degree + sin15degree 
20080501 

From meisje: sin105degree + sin15degree
Can you show me the steps and how to find the exact value? Answered by Stephen La Rocque. 





sin^2(x) = 2cosx 
20080426 

From Katelyn: I have been having some real trouble in trying to solve this equation:
sin^2(x) = 2cosx Answered by Stephen La Rocque. 





Sin^2x=1/2(1Cos2x) 
20080417 

From Chris: Could someone please show a step by step guide on how to answer this question
Sin^2x=1/2(1Cos2x) and then explain where this identity would be useful??? Answered by Harley Weston. 





5sin^2x+3sinx=4 
20080417 

From Chris: solve the following in the range 0  360 degrees?
5sin^2x+3sinx=4 Answered by Penny Nom. 





The height of a triangle 
20080417 

From Trent: I need to know the area of a triangle. One side is 5 the base is 12 and the angle between them is 52 degrees. No height is specified. How do I find the height to get the area? Answered by Penny Nom. 





Cutting a 200 diameter pipe at 45 degree angle 
20080410 

From Al: i want to cut a 200 diameter pipe in 45degrees. Can you demonstrate how to develop a flat rap around please Answered by Harley Weston. 





cosec [arccos (1/y)] 
20080409 

From Tom: I am having trouble with this question. For y > 1, the value of cosec [arccos (1/y)] is? Answered by Penny Nom. 





The integral of dx / (4x^2  25)^3/2 
20080401 

From Meghan: I have a question from the trigonometric substitution of my calculus course.
integral of dx / (4x^2  25)^3/2 Answered by Harley Weston. 





2 tan theta /(1 + tan^2 theta) = sin 2theta 
20080325 

From Charmaine: I'm having trouble on where to begin proving identities. I must prove that
(2 tan theta / 1 + tan^2 theta) = sin 2theta Answered by Penny Nom. 





The length of the ramp on a motorcycle trailer 
20080325 

From Joshua: I am currently building a motorcycle trailer. I am trying to figure out the length of the ramp so that the bikes don't scrap the trailer/ramp as they are loaded. This is the info I have: the motorcycle is 6" off the ground in the center, the point where the tires touch the ground are 80" apart, the trailer deck is 20" high. How do I figure the length of the ramp? Please show equation so I have for future reference with different measurements. Answered by Stephen La Rocque and Harley Weston. 





A hydraulic cylinder 
20080324 

From james: I am trying to adjust the placement of a hydraulic cylinder that raises a dump bed up from the frame of a truck.
How long would the cylinder (height of a triangle) have to be to raise the bed to a 70 degree angle?
The base from pivot to cylinder is 132.5 inches. Answered by Stephen La Rocque. 





The limit of (sin4x)/(tan9x) as x approaches zero 
20080314 

From stev: as x>0. How do you find the limit of f(x)=(sin4x)/(tan9X) Answered by Harley Weston. 





How tall is the tower? 
20080313 

From chris: you are standing 120 feet from the base of a tower. the angle of the elevation to the top of the tower is 15 degrees. how tall is the actual tower? Answered by Penny Nom. 





A dog and a fire hydrant 
20080306 

From Brittany: A bulldog is walking east along Main St. at a speed of 4 miles per hour. He wants to get to a fire hydrant on a parallel street. Initially, the bearing to the hydrant is south 62 degrees east. After 20 minutes, the bearing is south 41 degrees east. If the bulldog continues his walk, what is the closest he will be to the hydrant? Answered by Stephen La Rocque. 





cos(2x)=(cos x)^2 (sin x)^2 
20080225 

From azarnia: comment démontrer que : cos(2x)=(cos x)²_(sin x)² Answered by Maxime Fortier Bourque. 





lim sin 4x/sin 6x as x approaches zero 
20080222 

From josh: lim sin 4x/sin 6x
x approachs 0 Answered by Stephen La Rocque and Harley Weston. 





(1tanx) / (1+tanx) = (1sin2x) / cos2x 
20080214 

From isaiah: i'm having trouble proving 1tanx / 1+tanx = 1sin2x / cos2x, can anyone help me from going crazy? Answered by Penny Nom. 





cos t = 2 tan t 
20080206 

From peggy: cos t = 2 tan t. Find the value of sin t.
I can not solve this problem. I have the answer and some hints, but I need a step by step answer.
I really want to understand how this problem is solved. Answered by Stephen La Rocque. 





Angle of Elevation 
20080129 

From Rita: Uluru or Ayers Rock is a sacred place for Aborigines of the western desert of Australia.
ChunWei uses a surveying device to measure the angle of elevation to the top of the rock to be 11.5 degrees.
He walks half a mile closer and measures the angle of elevation to be 23.9 degrees.
How high is Ayers Rock in feet? Answered by Stephen La Rocque. 





The cosine of an angle 
20080121 

From Kristine: Find measure of unknown side
cosA=0.5 Answered by Harley Weston. 





Rewrite the expression in terms of cosine to the first degree 
20080114 

From Jamie: Hi. Im am having trouble with a problem on my math homework. I need help rewriting the expression in terms of cosine to the first degree.
(sinx)^4(cosx)^2 Answered by Harley Weston. 





Two solutions using the law of sines 
20080114 

From Kate: I am working on the Law of Sines and I have a problem that says: Find a value for b so that the triangle has 2 solutions.
I am given that A = 36 degrees and a = 5. Now, I learned that for a triangle to have 2 solutions, h < a < b.
BUT...my answer key says the answer is: 5 < b < 5/sin 36. I can't figure out how to make this fit with h < a < b. Answered by Harley Weston. 





cosX= 1.25 
20080110 

From Stephanie: Why isn't there really a solution for the equation: cosX= 1.25 ? Answered by Stephen La Rocque. 





sinX=cos2X 
20080107 

From Jennifer: sinX=cos2X
how do you solve for X? I'm frustrated I've forgotten how to solve this equation. Answered by Stephen La Rocque and Harley Weston. 





How far is the jet from the lighthouse? 
20080107 

From Natalie: Question: A ship spots a lighthouse that is 53m high, at an angle of elevation of 7 degrees that is directly north of the ship. The same ship spots a jet travelling N62E at an altitude of 1500m with an angle of elevation of 15 degrees. How far is the jet from the lighthouse?
Natalie Answered by Harley Weston. 





lim sinx/(x +tanx) 
20071216 

From shimelis: i have problem how do you solve this equation
lim sinx/(x +tanx) Answered by Harley Weston. 





sin^2x=1/2(1cos2x) 
20071212 

From katelyne: Hello there.. I was assigned a problem that I am having trouble with in my
PreCalc class and it is as follows:
sin^2x=1/2(1cos2x) Answered by Penny Nom. 





Solve sin(x)=x^2x 
20071211 

From ming: is there anyway you can solve
sin(x)=x^2x without a calculator? Answered by Stephen La Rocque. 





A triangle and a pentagon 
20071208 

From Olivia: A regular pentagon has an area of 800 square centimetres. What is the area of the triangle extended from one side of the pentagon? Answered by Stephen La Rocque. 





Area = 1/2 ab SinC 
20071203 

From Eileen: Given: Acute triangle ABC, with a, b, c, being the respective opposite sides to angle A, angle B, angle C, and altitude, h, drawn from angle B to b.
Prove: The area of trianlge ABC=1/2abSin C Answered by Stephen La Rocque. 





If x=18, prove that sin2x=cos3x. 
20071202 

From amy: If x=18, prove that sin2x=cos3x.
find the exact values of sinx and cosx Answered by Penny Nom. 





A trig identity 
20071128 

From Julia: sin4x 1  cos2x
 x  = tanx
1  cos4x cos2x Answered by Harley Weston. 





The definition of the sine function 
20071122 

From Indrajit: I need a explanation in this theory.......if sinθ = p/h...then
sin 90 deg. = p/h
or 1 = p/h
or p=h .....how can a perpendicular be equal to a hypotenuse.??? Answered by Harley Weston. 





A cylindrical tank 
20071116 

From Mario: I want to determine how many gallons i have inside a cylinder (tank) that is resting on its side (the Height), NOT standing up.
I know V=pi x r2 x H. And 1 cubic foot = 7.48 gallons. Here are the dimensions r=2' H=20'. Now my question is how do I determine how much
liquid i have inside, if the level of the liquid is about 1/2 of the way of its Diameter (in other words 2'). Remember this cylinder is lying
on its side. Answered by Penny Nom. 





Family of functions 
20071112 

From Russell: Consider the family of functions
f(t)= Asin3t + Acos3t +Bsin8t + Bcos8t
find exact values of parameters A and B so that f(0) = 2 and f ' (0) = 1 Answered by Stephen La Rocque. 





A trig identity 
20071110 

From James: I need to prove trig identities, and I can't figure this one out
1 + sinx  cosx 1  cosx
 = 
1 + sinx + cosx sinx
Answered by Chris Fisher. 





Is there a practical use for radian measure? 
20071026 

From Paula: Is there a practical use for radian measure in any profession? Which professions might us radian as opposed to degree measure? Answered by Harley Weston. 





(3)^1/2 * tan(t/3) = 1 
20071026 

From Rosie: Please help me with finding the solution to:
(3)^1/2 * tan(t/3) = 1. Answered by Penny Nom. 





1tan^3t/1tant=sec^2t+tant 
20071023 

From Brian: I need help proving:
1tan^3t/1tant=sec^2t+tant Answered by Harley Weston. 





lim (1 2 cosx) / (sin(x pi/3)) 
20071015 

From hanan: lim (1 2 cosx) / (sin(x л/3)) Answered by Harley Weston. 





A trig limit 
20071012 

From Amanda: What is the limit, as x tends to zero, of: (1cos(4x))/(xsin(x))?
Thank you!
~Amanda Answered by Harley Weston. 





Irrational functions 
20071001 

From alicia: i have a question about irrationals functions.
i have been using them quite some time now, but i wonder where they can be found in daily life?
i hope you can help me, Answered by Harley Weston. 





32 cis30degrees / 4 cis150degrees 
20070921 

From Michael: Could you please help with this one.
32 cis30degrees / 4 cis150degrees Answered by Stephen La Rocque. 





A trig problem 
20070916 

From Tracy: I have a scalene triangle ABC, angle C is 20 degrees, side AC is 8cm and side AB is 3 cm.
Line CB is extended to point D which is perpendicular to point A, triangle ABD is a rightangled triangle.
How do I calculate length of line AD Answered by Stephen La Rocque. 





The elevation of the sun 
20070910 

From Elena: The "angle of elevation" of an object about you is the angle between a horizontal line of sight between you and the object. (See figure) After the sun rises, its angle of elevation increases rapidly at first, then more slowly, reaching a maximum near noontime. Then the angle decreases until sunset. The next day the phenomenon repeats itself. Assume that when the sun is up, its angle of elevation (E) varies sinusoidally with the time of day. Let t be the number of hours that has elapsed since midnight last night. Assume that the amplitude of this sinsoid is 60 degrees, and the maximum angle of elevation occurs at 12:45 p.m.. Assume that at this time of year the sinusoidal axis is at E=5 degrees. The period is, of course, 24 hours.
a. Sketch a graph of this function
b. What is the realworld significance of the t  intercepts?
c. What is the real world significance of the portion of the sinusoid, which is below the taxis?
d. Predict the angle of elevation at 9:27 a.m., and at 2:30 p.m.
e. Predict the time of sunrise
f. As you know, the maximum angle of elevation increases and decreases with the change of the seasons. Also, the times of sunrise and sunset change with the seasons. What one change could you make to your mathematical model that would allow you to use it for predicting the angle of elevation of the sun at time on any day of the year. Answered by Harley Weston. 





Where do you use trigonometry? 
20070821 

From jenny: where do you use trigonometry besides architecture and engineering? Answered by Stephen La Rocque. 





How many complete cycles does the piston make in 30minutes? 
20070811 

From San: A piston in a large factory engine moves up and down in a cylinder.
The height, h centimetres, of the piston at t seconds is given by formula
h=120sin(pi)t+200
How many complete cycles does the piston make in 30minutes? Answered by Penny Nom. 





Trig identities 
20070730 

From Suzanne: I'm a UR University Graduate (with High honours!) but not in math: I'm taking GeoTrig, Sk Learning version, and the text is poorly written. But I was flying through the material until I hit the Trig Identities. I just don't get WHY we have them, why we should know them? What good is this "theory". All that "simplying" rarely yeilds a simpleer version! Also, give me advice for how to study them.
Thanks
Suzanne Answered by Harley Weston. 





Angle of depression 
20070723 

From joyce: hello,
here is my problem......
As you stand on a bridge w/c is 100 ft. above the water
you are looking @ an approaching barge.
If the A of top of the front of the bridge is 29.04 degrees
and the angle of depression of the rear is 17.36 degrees .
Find the length of the barge? Answered by Harley Weston. 





Some trig problems 
20070720 

From Jocelyn: I wasn't able to solve this equation:
only find the function using Pythagorean theorem
Please help me....
sinA = 3/4 find secB
tanA = 3/4 find cosA
sinB = 4/5 find tan A
cosA = 5 find csc A
b =5; a= 12 find sin A
c =25; a = 24 find cot A
a = 6; c =10 find b?
Find B when c = 25; a = 24
Find A when a = 5 and b = 12
csc = 1/2 find cos Answered by Penny Nom. 





Trig functions for angles not between 0 and 90 degrees 
20070716 

From Tim: My question: Why is the value of a trigonometric function, the same, for an angle over 90 degrees and its reference angle?
How are the angle and its reference related? Do they both form a triangle that has equal sides? Answered by Penny Nom. 





Another trig limit 
20070716 

From Richter: lim (π + x)/[cos(x/2)]
x>π Answered by Harley Weston. 





A trig limit 
20070716 

From Richter: what is the value of lim [cos (π/x)]/(x2) as x>2? Answered by Harley Weston. 





Trig identities 
20070705 

From Alex: Use the identities tan_=sin_/cos_ and/or sin*_+cos*_=1 to simplify 1cos*_ Answered by Stephen La Rocque. 





Period of a sum of trig functions 
20070617 

From Aakash: the period of the function f(x)=cos3x+sin4x+tan4x Answered by Stephen La Rocque. 





How high does the ladder reach? 
20070611 

From Madi: A ladder 8 ft long resting on a house makes a 60 degree angle with the ground. how far up the house does it reach? Answered by Stephen La Rocque. 





A flagpole and a telescope 
20070604 

From Fabiola: A telescope is mounted on a tripod 5 ft above the ground and 20 ft from a
flagpole. The telescope must be rotated 48° from horizontal to see the top
of the flagpole. How tall is the flagpole? Answered by Stephen La Rocque. 





Finding the hypotenuse without Pythagorus 
20070511 

From Shelbie: How do i find the hypotenuse of a right traingle not using the pythagorean thereom if i have the measurements of the legs? Answered by Stephen La Rocque. 





Angle of Elevation 
20070510 

From Micky: Two Buildings are on opposite sides of a street 40 feet wide.
The taller of the two buildings is 580 feet tall. The angle of depression
from the top of the tallest building to the shorter building across the
street is 57 degrees. Find the height of the shorter building. Answered by Stephen La Rocque. 





Find the real solutions in this trig equation 
20070509 

From tony: list all real solutions of the equation that are in the interval [0,2π)
2cos(x) + tan(x) = sec(x) Answered by Penny Nom and Stephen La Rocque. 





Evaluating sine and cosine 
20070506 

From Selimovic: How can i solve sine or cosine for angle of, lets say 10°....Maybe
it's easy but i don't know how... Answered by Penny Nom. 





A couch sliding off a truck 
20070430 

From William: A couch with a mass of 1 X 10^2kg is placed on an adjustable ramp connected to a truck. As one end of the ramp is raised, the couch begins to move downward. If the couch slides down the ramp with an acceleration of .70 meters per second when the ramp angle is 25 degrees, what is the coefficient of kinetic friction between the ramp and couch?
I drew a force diagram and if I did it correctly I identified the forces involved as "mg" (mass x gravity), "Fn" (normal force) and the "Ff" (frictional force). I know that we have the couch sliding down the ramp a .70 m/s but I don't think this a force and I'm not sure how this info fits into the problem. I know that the formula for calculating the coefficient of friction is Ff/Fn. Based upon the force diagram I drew and calculated Fn to be 1082N. I can't seem to get past this point. How do I determine what the frictional force is? Answered by Stephen La Rocque. 





Constructing an octagonal deck around a circular pool 
20070420 

From Cliff: [I am building an] octagonal desk encompassing 17 foot diameter circle for pool.
I have seen other octagonal calculations but none of these tell me how much allowance for a circle to fit within the octagon without losing the circle edge can anyone help
thanks cliff Answered by Stephen La Rocque. 





y = cos(2x) and y = 0.5 
20070415 

From kassandra: Sketch the graphs of y= cos 2x and y= 0.5 over the domain pi < x
I was wondering if someone could check it for me thanks! Answered by Penny Nom. 





Graphs of trig functions 
20070413 

From taylor: The following graph represents a sine function in the form
y=A sin B(x+C) +D or a cosine function in the form y=A cos B(x + C) +D. Write an equation of the graph in both forms Answered by Stephen La Rocque. 





sin(2x) = cos(3x) 
20070404 

From ben: find all positive angles x such that 3x is one of the nonright angles in a right triangle and sin(2x) = cos(3x). Answered by Stephen La Rocque and Penny Nom. 





Boat trigonometry 
20070404 

From Kimi: Hi,
I have been working on the attached math problem for my college trig class for over a week. Every avenue I've tried seems to lead either to a dead end, an unreasonable answer, or extremely complicated computations. I was able to calculate the speed of the boat to 3.51 mph, but cannot figure out the measure of angle beta. Once I can figure that out, I can do the rest of the problem.
Thanks,
Kimi Answered by Stephen La Rocque. 





Friction of a skier 
20070324 

From William: An olympic skier moving at 20.0 m/s down a 30 degree slope encounters a region of wet snow and slides 145m before coming to a halt. What is the coefficient of friction between the skis and the snow? Answered by Stephen La Rocque. 





The distance between two fire towers 
20070323 

From tony: Two fire towers are 30km apart, tower A is due west of tower B. A fire is spotted from the towers, and the bearing from A and B are N76degreesE and N56degreesW, respectively. Find the distance from the fire to the straight line connecting tower A to tower B. Answered by Stephen La Rocque. 





Angles of depression 
20070321 

From romaine: a woman of height 1.4m standing on top of a building of height 34.6m veiws a tree some distance away.
she observes that the angle of depression of the bottom of the tree is 35 degrees, and the angle of depression of the top
of the tree is 29 degrees. assume that the building and the tree is on level ground.
(a) calculate the distance of the woman from the top of the tree measured along her line of sight.
(b) determine the height of the tree. Answered by Stephen La Rocque. 





A river crossing 
20070316 

From tara: A river has a constant current of 4 kilometers per hour. At what angle
to a boat dock should a motorboat, capable of maintaining a constant
speed of 20 kilometers per hour, be headed on order to reach a point
directly opposite the dock? If the river is 1/2 kilometer wide, how long
with it take to cross? Answered by Stephen La Rocque. 





Triple angle tangent formula 
20070315 

From sam: Hi I am trying to derive a triple angle formulae for tan. I know i need to use compound and double angle formulae but am finding it difficult to "clean" up my fraction to get the triple angle formulae can you show me a worked derivation?! thanks Answered by Penny Nom. 





Angle of elevation 
20070313 

From Joslyn: A ship at sea sights a 12m high lighthouse on a cliff which is 80m above sea level.
If the angle of elevation to the top of the lighthouse is 27 degrees, calculate the distance from the ship to the shore. Answered by Haley Ess. 





A trig limit 
20070311 

From Lo: tan(2*x)/sin(3*x) Answered by Penny Nom. 





sin(3a), cos(3a) and tan(3a) 
20070228 

From mailene: hi, i...indeed,to..need..your..help how..cn..i..prove..this,formula??? sin3a=3sina4sin^3a cos3a=4cos^33cosa tan3a=3tantan^3a /13tan^2a the..symbol...^is..the..expOnent Answered by Haley Ess and Penny Nom. 





Trig  Ferris wheel 
20070213 

From Anthony: A ferris wheel is 250 feet in diameter and revolves every 40 seconds when in motion. Your step up to seat on the wheel at the bottom 2 feet above the ground so you are sitting 4 feet above the ground to start. Derive the formula for the height of your seat at time (t). If I go three times around, how long is the ride in ditance traveled? Answered by Stephen La Rocque and Penny Nom. 





tanx (cotx + tan x ) = sec^2x 
20061230 

From Fren: tanx (cotx + tan x ) = sec^2x Answered by Penny Nom. 





A trig identity 
20061228 

From Courteny: Prove that 1  cos 2x + sin 2x (divided by) 1 + cos 2x + sin 2x = tan x Answered by Penny Nom. 





cos 2a+cos4a+cos6a=? 
20061215 

From Saban: cos 2a+cos4a+cos6a=? Answered by Steve La Rocque, Chris Fisher and Penny Nom. 





A trig identity 
20061214 

From Zamira: i need help with this proof: ((cot(x)tan(x))/ cot(x) + tan(x)) = cos (x) Answered by Penny Nom. 





Sin 2x / 1Cos 2x = 2 Csc 2x  Tan x 
20061206 

From Mark: I need to prove the following: Sin 2x / 1Cos 2x = 2 Csc 2x  Tan x Answered by Steve La Rocque. 





cos2x=1 
20061121 

From Christina: I'm have a hard time solving cos2x=1 for exact values between 0<_x <360 Answered by Stephen La Rocque and Penny Nom. 





tan1/2x + cot1/2x = 2cscx 
20061104 

From Jazmin: Prove tan1/2x + cot1/2x = 2cscx Answered by Penny Nom. 





Finding the legth of a guy wire 
20061015 

From Aubrey: a radio tower 500 feet high is located on the side of a hill with an inclination to the horizontal of 5 degrees. how long should two guy wires be if they are to connect to the top of the tower and be secured at two points 100 feet directly above and directly below the base of the tower? Answered by Stephen La Rocque. 





How high (in feet) is the mountain? 
20060829 

From Briana: A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, they observe that the angle of elevation to the top of the mountain is 29 degrees. From a point 2000 feet closer to the mountain along the plain, they find that the angle of elevation is 31 degrees.
How high (in feet) is the mountain? Answered by Stephen La Rocque. 





The development of trigonometry 
20060815 

From Eugene: Can you please give the exact time line of trigonometry. Answered by Penny Nom. 





A perpendicular intersection of two barrel vaults 
20060721 

From Neal: I'm wanting to build a series of architectural models of different roman and medieval buildings out of cardboard. Once I have perfected the models I want to print them out on card stock so that school kids (or anyone else) can make the buildings.
A feature of many of these models is the cross or groin vault (a perpendicular intersection of two barrel vaults).
A single barrel vault is easy to imagine as a plane (a rectangular piece of cardboard) that will be folded into a semicircular arch.
The intersection of a second barrel vault and this one is presenting me with problems. The second plane needs to have an ellipse cut into it so that when it is folded into the arch, it will mate up with the curve of the first barrel vault.
Given that the two pieces of card have identical widths (and therefore identical arcs in cross section) is there a way to calculate the ellipse that needs to be cut so that it can be cut before the second arch is folded? Answered by Edward Doolittle. 





Calculating the belt length of a three pulley system 
20060716 

From Mark: I have a 3 pulley system with sides abc and pulleys ABC. Pulley A has radius of 10cm, pulley B has radius of 20cm, and pulley C has radius of 3cm. The side lengths are: (center to center of pulleys) between pulleys AB = 75cm, between pulleys BC = 100cm, and between pulleys AC = 50cm. I set these side lengths up as (according to law of sines and cosines) a = 100cm, b = 50cm, and c = 75cm. What is the length of the belt required for this system? I need to know how I would set this problem up and solve. Answered by Stephen La Rocque. 





A problem with arc sine 
20060707 

From Scott: How to prove arc sin x = arc tan( (x)/√(1x2))
Answered by Penny Nom. 





A trig problem 
20060624 

From Greg: A and B are two towers, B being 4 km due east of A. The true bearings of a flagpole, C, from A and B are α east of north and α west of north respectively. The true bearings of a second flagpole, D, from A and B are (α + β) east of north and (α  β) west of north respectively. Assuming A, B, C, and D are on level ground, and that α = 25, β = 10, find the distance between C and D. Answered by Penny Nom. 





The area of a sector and a triangle 
20060623 

From Howard: I thought of the following problem which is similar but much simpler than the tethered goat problem: What is the angle(it is more illustrative in degrees)of arc of a unit circle so that the area between the chord it subtends and the arc length is equal to the area of the triangle with opposite side the subtended chord. Answered by Stephen La Rocque and Penny Nom. 





find the height of the tower 
20060617 

From Evelyn: The angle of elevation from a point 89.6' from the base of a tower to the top of the tower is 42'40'... find the height of the tower Answered by Penny Nom. 





What is the value of csc (2pi/3)? 
20060604 

From Kishor: What is the value of csc (2pi/3)? Answered by Stephen La Rocque. 





A trig identity 
20060604 

From Courtney: Show that this equation is an identity:
(sin x + sin 2X)/(cos x  cos 2x) = cot(x/2) Answered by Stephen La Rocque. 





A limit involving trigonometry 
20060502 

From Allie: My question is how do you solve.
lim as t goes to 0 [sin squared *3t] / t squared? Answered by Penny Nom. 





Finding the side of a triangle 
20060406 

From Carole: okays, well, im having difficulty finding the side of a triangle. It is a right triangle and the information given is that the hypotonous is 24 and the angle adjacent to the 90 degree is 32. Im trying to find X, which is placed on the bottom leg of the triangle, and have no idea how to do it. can you explain to me how to get the answer, please? i'd like to know for future reference, please. thank you. Answered by Stephen La Rocque. 





Two trig questions 
20060404 

From mandy: I have a few questions that I need help with for my precal class in college. The following have to prove the trigonometric identities:
cos^{4}x + 2cos^{2}x sin^{2}x + sin^{4}x = 1
sin^{4}x  cos^{4}x = 1  2cos^{2}x
thanks you, Answered by Stephen La Rocque. 





cos(3X) 
20060329 

From Joshua: I'm having trouble proving that cos(3X)=cos^{3}X (cosX)(sin^{2} X) Answered by Penny Nom. 





A trig identity 
20060328 

From Iqbal: Could you please prove,
[tan(x)sin(x)]/sin^{3}(x)=sec(x)/[1+cos(x)]
Answered by Stephen La Rocque. 





Solve the equation cos x = sin 20 where x is acute. 
20060326 

From Elle: Solve the equation cos x = sin 20 where x is acute. Answered by Stephen La Rocque. 





The waterway between Lake Huron and Lake Superior 
20060321 

From Trenae: the waterway between lake huron and lake superior separates the u.s and canada.it is usually 13 feet above the water when its closed and each section is 210 feet long if the angle of elevation is 70 degrees then what is the distance from the top of the drawbridge to the water and the width of the gap created by the 2 sections of the bridge Answered by Penny Nom. 





Find the ground speed and the planes true heading. 
20060205 

From Jimmie: An aircraft going from city A to city B on a bearing of S69E (degrees) is traveling at a speed of 430 mph. The wind is blowing out of the north to south at a speed of 25 mph. Find the ground speed and the planes true heading. Answered by Penny Nom. 





A trigonometric identity 
20060122 

From Sarfaraz: Prove the following trigonometric identity.
sin^{2}x = tan^{2}x/(1+tan^{2}x) Answered by Penny Nom. 





The height of a right triangle 
20051221 

From Sanmantha: I am trying to solve for the height of a right triangle. The base is .05 mm, and the apex is 0.5 degrees. I vaguely recall from high school that this should be enough information to solve for height, but I can't remember what equation(s) to use. Answered by Penny Nom. 





A regular octagon is inscribed in a circle 
20051213 

From Carlin: A regular octagon is inscribed in a circle of radius 15.8 cm. What is the perimeter of the octagon? Answered by Penny Nom. 





A pair of trig equations 
20051205 

From Kevin:
I am trying to solve for A and B but haven't been able to find a trig identity that will help me.
1.414 = .5cosA + cosB
.5 = .5sinA  sinB
how do I solve this?
Answered by Penny Nom. 





How is trigonometry applied to everyday life? 
20051203 

From Yadira: My question is how is trigonometry applied to everyday lives and functions. Ex: Builders use it but how and what are some examples of the trigfunctions or formulas that they use? Answered by Harley Weston. 





The elevation of the top of the house 
20051113 

From Chloe: Karen is standing 23 metres away from the base of a 23 metre high house. Assume that Karen's eyes are 1.5 metres above ground. Find the elevation of the top of the house from Karen's eye line. Answered by Penny Nom. 





The height of a tower 
20051108 

From Vinita: Observers at point A and B, who Stand on level ground on opposite sides of a tower, measure the angle of elevation to the top of the tower to be 33 degrees and 49 degrees respectively. Another point C is 120 m from point B, Triangle ABC =67 degrees and BAC = 31 degrees. Find the height of the tower to the nearest metre. Answered by Penny Nom. 





The length of a chord 
20051103 

From Sue: How do you determine the length of a chord when given the diameter of the circle (1.6m) and that the angle = 7π/8 Answered by Penny Nom. 





sin(kx) = x 
20051020 

From David: What is an integer value for k so that sin(kx) = x has exactly 2005 solutions? How does one arrive at the answer? Answered by Harley Weston. 





Determine the height 
20051014 

From Paul: if you know the distance to the base and the angle to the top how can you determine the height Answered by Penny Nom. 





Elliptic trigonometry 
20050915 

From Krystal: I'm currently searching for a science project topic and i have the idea of deriving elliptic trigonometry analogous to circular trigonometry. My questions are:
Is this project "possible" to do? Answered by Chris Fisher and Harley Weston. 





The length of a chord 
20050908 

From A student: how do you find the length of a chord given the angle and radius of the circle Answered by Penny Nom. 





cos x * cos 2x * cos 4x * cos 8x 
20050829 

From Leandro:
A = cos x * cos 2x * cos 4x * cos 8x
What's the value of log A at base 2?
Answered by Chris Fisher and Penny Nom. 





A television antenna sits on a roof. 
20050730 

From Liz: A television antenna sits on a roof. Two 76foot guy wires are positioned on opposite sides of the antenna. The angle of elevation each makes with the ground is 24 degrees. How far apart are the ends of the two guys wires? Answered by Penny Nom. 





The value of n*tan*(180/n) tends to pi 
20050711 

From Daniel: I am 14 and i have been given a piece of maths coursework whereby a farmer has to fence off a piece of land as large as possible using 1000m of fence. I already know that the formula for working out the area of any shape of a 1000m perimeter = 500^{2}/ n*tan*(180/n), however, after some research I have found out that as the number of sides (n), tends to infinity, the n*tan*(180/n) tends to pi. Why is this? Answered by Penny Nom. 





arccos(5/13) 
20050531 

From Kyle: I would like to know how to evaluate the problem of: Arccos 5/13. Answered by Penny Nom. 





sin x + sin 2x + sin 3x + sin 4x = 0 
20050510 

From Elia: I tried many times, but can't get to solve the following question:
sin x + sin 2x + sin 3x + sin 4x = 0 Answered by Chris Fisher. 





cos(2x) = sin(3x) 
20050414 

From A student: Show that if x= 18 degrees, then cos2x =sin 3x. HENCE find the exact value of sin 18 degrees, and prove that cos 36  sin 18 =1/2. Answered by Andrei Volodin, Claude Tardif and Penny Nom. 





tan55.tan65.tan75=tan85 
20050330 

From Jesus: My name is Jesus and I´m a secondary student. I´m trying to verify a trigonometric identity but I don´t know how to do it.please help me!!!!!!!!!.
The identity is : tan55º.tan65º.tan75º=tan85º (the sign (.) indicates multiplication)
Answered by Chris Fisher and Penny Nom. 





A wishing well 
20050328 

From Don:
I am building a wishingwell
out of pieces of 2by4. I have included a picture of a miniature version
of what I want. There are to be ten 2by4 pieces around the well and
I want the circle around the outside of the structure to have a diameter
of approximately 3 feet. How long to I cut the 2by4's to build the
wishingwell.
Thanks,
Don
Answered by Harley Weston. 





Find the height of the pole 
20050322 

From Dorothy Jean: From the top of a building 70ft.high, the angle of elevation of the top of the pole is 11.2 degrees. From the bottom of the building the angle of elevation of the top of the pole is 33.4 degrees. Find the (a) height of the pole and (b) the distance from the building. Answered by Penny Nom. 





A trig identity 
20050306 

From Patrick: im trying to verify this
identity:
sin(x)+sin(5x)
 = tan(3x)
cos(x)+cos(5x)
Answered by Chris Fisher. 





cos 2x = sin x 
20050122 

From Kris: solve the equation
cos 2x = sin x for 0<= x < 360 Answered by Penny Nom. 





Finding the missing side of a triangle 
20050120 

From Jason: I found a geometry problem that reads as follows:In triangle ABC, Answered by Penny Nom. 





The angle between two forces 
20050119 

From Abraham: One force of 20 pounds and one force of 15 pounds act on a body at the same point so that the resultant force is 19 pounds. Find, to the nearest degree, the angle between the two original forces. Answered by Penny Nom. 





The tide at a boat dock 
20050111 

From Abraham: The tide at a boat dock can be modeled by the equation
y = 2cos(pi/6 t) + 8,
where t is the number of hours past noon and y is the height of the tide, in feet. For how many hours between t=0 and t=12 is the tide at least 7 feet? Answered by Penny Nom. 





Modelling monthly temperature with a cosine 
20041225 

From Regis: The average monthly temperature for a location in Ontario as a function of month number can be modelled using the equation y = a cos[k(t + b)] + d. Answered by Harley Weston. 





sin(3A) 
20041020 

From A student: Express sin3A in terms of sinA and cosA. Answered by Penny Nom. 





X is due north of Y ... 
20040811 

From A student: X is due north of Y and 2km distant. Z is due east of Y and has a bearing of S35°12'E from X. How far, to the nearest metre, is Z from X? Answered by Penny Nom. 





Two trig problems 
20040804 

From Tracie: sin^2x  sin x 12 = 0
sin 2x = sin x Answered by Penny Nom. 





A trig problem 
20040802 

From A student: Given that the maximum value of [sin(3y2)]^2 [cos(3y2)]^2
is k. If y>7, Find the minimum value of y for which
[Sin(3y2)]^2  [cos(3y2)]^2 =k. Answered by Penny Nom. 





The height of a building 
20040616 

From Lauren: I have a homework assignment to measure a building on my school's campus. I have to stand at least 40 ft away from the building and find the angle of elevation from my feet to the top of the building. Then I have to walk at least 40 ft form that point, record the distance as X, and find the angle of elevation from my feet to the top of the building. Using X and the angles, I have to determine the height of the building. I used a protractor and a weighted string to find the angle of elevation from my eyes to the top of the building. But I haven't been able to find the way to measure the angle of elevation from my feet to the top. Answered by Penny Nom. 





Programming without trig functions 
20040525 

From Derek: I am a programmer trying to calculate the following.
What is the formula to find the crosssectional area of a cylinder with out using any trig functions? or better yet, how can you calculate any given volume in a cylindrical tank with spherical heads with out trig functions?
I am using a PLC (programmable logic controller) to do this and trig functions are not available. Answered by Harley Weston. 





Some trig expressions 
20040523 

From A student: Prove:
sin A + sin B = 2sin(A+B/2)cos(AB/2)
cos A  cos B = 2sin(A+B/2)sin(AB/2)
cos A + cos B = 2cos(A+B/2)cos(AB/2)
sin A  sin B = 2cos(A+B/2)sin(A+B/2) Answered by Penny Nom. 





An oildrilling platform 
20040427 

From Alie: An oildrilling platform is located in the Gulf of Mexico 3.25 miles from the nearest point on shore. From a point B on the shore due east of A the bearing of the platform is S51.2W. How far is it from B to the platform? Answered by Penny Nom. 





The height of a building 
20040331 

From Nat: Two buildings are 26.3m apart. From the top of the shorter building the angle of elevation to the top of the taller building is 35.9 degrees and the angle of depression to the base of the taller building is 54.7 degrees. What is the height of the taller building? Answered by Penny Nom. 





Cosine of 35 degrees 
20040303 

From Jason: How do you find the exact solution to cosine 35 degrees. Answered by Chris Fisher. 





Proof by induction 
20040302 

From Chris: I need some help of how to solve the problem
"use the principle of mathematical induction to prove that the following are true for all positive integers"
cos(n x pi + X) = (1)^n cosX
any help would be appreciated Answered by Penny Nom. 





Sin(3x), cos(3x) and tan(3x) 
20040128 

From Jon: What is the identity for cos3x, sin3x, and tan3x? In class, we learned double angel identities and were asked to find out the identity to these three trig functions. If you can help, please do. Also, i know that the cos^{4}x sin^{4}x is the same as cos2x. Is cos^{8}xsin^{8}x = cos2x also true? Thank you.s Answered by Chris Fisher. 





Some trig problems 
20040118 

From Weisu:
I have some questions about precalculus.
(1) (2(cos(x))^2)+3sin(x)1=0
(2) sin(x)cos(x)=(1/2)
(3) 3sin(x)=1+cos(2x)
(4) tan(x)*csc(x)=csc(x)+1
(5) sin(arccsc(8/5))
(6) tan(arcsin(24/25))
(7) arccos(cos(11pi/6))
the last problem uses radian measure.
Answered by Penny Nom. 





Finding angles 
20031202 

From Jason: I AM TRYING TO SOLVE A TRIG PROBLEM AND HAVE
FORGOT HOW TO DO IT. WHAT I HAVE IS A RIGHT TRIANGLE WITH SIDE A BEING 14
FEET AND SIDE B BEING 3 FEET, USING PYTHAGOREAMS THEOREM SIDE C SHOULD
EQUAL 14.318 FEET ON A RIGHT TRIANGLE BUT I AM TRYING TO REMEMBER HOW TO
FIND MY ANGLES OTHER THAN THE ONE THAT IS 90 DEGREES. Answered by Penny Nom. 





Laws of sines and cosines 
20031123 

From A parent: On the one side of a stream lines PA= 586.3 feet, PB = 751.6 feet are measures, angle APB being 167 degrees and 36 min. Q is a point on the opposite side of the stream. Angle PAQ=63 degress and 18 min and PBQ=49 degrees and 24 min. Find PQ. Answered by Penny Nom. 





A trig identity 
20031112 

From A student: I can't prove this identity. Can you please help me? (1tanx)/(1+tanx)=(1sin2x)/(cos2x) Answered by Penny Nom. 





Two precalculus problems 
20030804 

From Kate:
Please help me verify the identity: cos2x(sec2x1)=sin2x Also I am having trouble withdetermining whether f(x) is odd, even, or neither f(x)=x3x Answered by Penny Nom. 





Odd powers of sine and cosine 
20030625 

From Antonio: Can you please tell me how to integrate a trig function involving sine and cosine? I know if the powers of both the sine and cosine are even and nonnegative, then I can make repeated use of the powerreducing formulas. But for the question I have on my hand, the powers of both sine and cosine are odd: ( sin3x + cos7x ) dx. Answered by Harley Weston. 





Two trig problems 
20030610 

From Bett:
I have this ongoing trouble with trig and solving triangles with laws of cosines and sines!! For example if it asks to solve triangle FGH, given angle G=102.7 , side f=14.2, and h=18.6. Now do I use law of cosines because I don't have the measure of an angle and length of the opposite side??I don't know where to go from here,I am totally confused!!! I also have a problem with this word problem I have been doing. It asks: An airplane flies 847.5 km at a bearing of 237.3 degrees. How far south and west fo its original position is it? Huh? Please help! Answered by Penny Nom. 





A trig identity 
20030520 

From Patty: Please help with the following
1/ tanx + cotx = sinxcosx Answered by Penny Nom. 





sin theta = 7/8 
20030507 

From Patty: If sin0 = 7/8 and 0 is in quadrant 2, find the other five trigonometric functions of 0. (report your answers in radical form) Answered by Penny Nom. 





Write sin(3x) in terms of sin(x) 
20030505 

From A student: Write sin 2x in terms of sin x Answered by Penny Nom. 





Three proffs of a trig identity 
20030318 

From Nadene: Prove the identity. cos [x + (ypi/2)] = sin (x+y)
A hint was also provided which is: "Apply cos (alpha + beta) first then within that apply cose (alphabeta)" Answered by Penny Nom. 





A trig identity 
20030222 

From Ron: We have spent hours trying to solve the following identity without success. Can you give us some hints as to how it is done?
1 + tan(x) tan(2x) = tan(2x) cot(x) 1 Answered by Penny Nom. 





Radians 
20030116 

From Erikson: I am a student in the 10th grade and attending advanced math at my high school. I was assign to do a report about the unit circle and the radian. But there seems to be no information available about the history of the radian; who first found out about them, which civilizations used it if any. Well, hopefully you'll assist me in this troubling question. Thank you for your kind consideration. Answered by Penny Nom. 





y = 1  sin(x + 60) 
20021210 

From Eman: Sketch the graph of y = 1  sin(x+60). for 0 <= x<= 360, giving the coordinates of the maximum and minimum points and the pints where the curves crosses the y axis. Answered by Penny Nom. 





Trigonometry 
20021201 

From Lance: My question is:
FIND ALL SOLUTIONS cosx=1sin(x/2) if x[0,2pi)
ALSO:
Given cscx=5/4 and cot>0, find csc(x/2) and cot(x/2) Answered by Penny Nom. 





Trigonometry problems 
20021201 

From Chiara:
 Find tan 35pi/4
 Graph y = cos^{2}x  2sinx
Answered by Penny Nom. 





An identity? 
20021027 

From Jenna: I can't prove
1sinQ 1  = tanQ +  1+sinQ cosQ
Answered by Penny Nom. 





An identity in trigonometry 
20021017 

From Alex: I really need help with proving this identity. (1+cosx+sinx)/(1+cosxsinx) = secx + tanx Answered by Penny Nom. 





A Circle is evenly divided into six equal triangles 
20020916 

From Marilynn: A Circle is evenly divided into six equal triangles leaving an area between the outside of the circle and the one side of the triangle. This area is measured as 3.14. What is the length of the radius, one line on the triangle? Answered by Paul Betts. 





The tangent to a curve and the tangent of an angle 
20020826 

From A teacher: Is there a relationship between the tangent of a curve(line touching the curve at one point) and tangent (the trigonometric function)? Answered by Chris Fisher. 





How far apart are the transmitters? 
20020518 

From Jeff: A ship at sea is 70 miles from one transmitter and 130 miles from another. The measurement of the angle between the signals is 130 degrees. How far apart are the transmitters? Answered by Penny Nom. 





The law of cosines and obtuse angles 
20020509 

From Bryant: The question that I am pondering is that I need to derive the law of cosines for a case in which angle C is an obtuse angle. Answered by Penny Nom. 





An identity(?) 
20020502 

From A student: prove identity sin^{ 2}x/1sinx= secx+1/secx
Answered by Paul Betts. 





A triangle in a circle of radius 6 
20020326 

From Marko: In a circle of radius 6, a triangle PQR is drawn having QR = 8 and PQ = 10. Determine the length of PR Answered by Chris Fisher. 





A trigonometric identity 
20020322 

From Debby: I am stuck on a problem and wondering if you can help?? It is: Prove the following: sec^{2}(X)+csc^{2}(X) = sec^{2}(X)csc^{2}(X) Answered by Harley Weston. 





sin 2x = cos 3x 
20020225 

From Allan: solve: sin 2x = cos 3x Primary question: how do you handle the cos 3x? Answered by Paul Betts and Chris Fisher. 





The size of a lot 
20020126 

From Claudia: I own a piece of property that I need to know the square feet for assessment purposes. The figure they came up with is wrong. They measured from one point to another and halved the sums but that means I own the cul de sac and we don't. My lot is 55 feet wide and one side is 108.96 feet and the other side is 146.04 that extends all the way to a circle. The front of the lot on the cul de sac is stated on the survey like this. 78.21 feet where R=40 feet. This large arc is taken off the size of our land. How many square feet is our lot. Answered by Harley Weston. 





Some trig problems 
20020122 

From Grant:
Solve each problem for theta(there is no sign on my computer)for 0 is less than or equal to theta which is less less than 360  2cosx1=0
cosx=1/2 Anwser 60,300
 tanx2sinxtanx=0
tanx(2sin+1)=0 (factor ?) tanx=0 and sin= 1/2 (solve from there?)
 2sinxcscx=0
2sinx1/sinx=0 3sinx1=0 3sinx=1/3(?)
 4cos(2x)+2cosx= 1
8cosx+2cosx+1=0 10cosx+1=0 10cosx= 1/10 (?)
 cos(2x30)=1/2
cos2xcos30=1/2 cos2xcos301/2=0 i don`t know what to do know
 Sinx+cosx=0
Square both sides? Answered by Claude Tardif. 





The tangent function 
20020112 

From Justine: if you know that sin45degress = cos45degrees, how do you know that tan45degrees = 1? Answered by Penny Nom. 





An octagon inscribed in a circle 
20020110 

From Kent: A circle of 30 in. diameter has an octagon (8 equal chords) inscribed in it. What is the length of each chord? Answered by Chris Fisher. 





A 3 dimensional 5 pointed star 
20011108 

From Kent: I am looking for a formula that will give me a layout for a 3 dimensional 5 pointed star. I want to form it out of sheet metal, using 5 polygons and soldering them at the apex. Can you please help me with this? I would like to be able to give the formula the height of the star from the bottom two points to the top point and also how deep the star is. Thank you very much! Answered by Judi McDonald. 





3pi/2  pi 
20011029 

From Karen: I need to simplify this a) 3pi/2  pi Answered by Penny Nom. 





e^{ix} = cosx + isinx 
20011010 

From Peter: Given: e^{ix} = cosx + isinx  substitute x for x to find e^{ix}, simplifying your answer
 use the given and part a to find an identity for cosx making no reference to trig functions
 find an identity for sinx
 .
 .
Answered by Penny Nom. 





Solving trig equations 
20010922 

From Asad: Can you please explain to me how to solve trig Equations,e.g sin(x)=x^{4}+12/2+cos(x)=x^{6}+9/3= (if this can be solved) Answered by Claude Tardif. 





Standard angles 
20010805 

From Nagaraj: Why 0^{o} , 30^{o} , 45^{o} , 60^{o} ,and 90^{o} are taken as standard angles in Trigonometry? Why can't we take some other angles as standard angles? Answered by Chris Fisher. 





The radius of a planet 
20010730 

From Jessica: A satellite is orbiting the earth at an altitude of 100 miles. If the angle of depression from the satellite to the horizon is 50 degrees, what is the radius (to the nearest mile) of the planet? Answered by Harley Weston. 





A trig identity 
20010727 

From Jeff: prove this identity and show steps tan(x/2+pi/4)=secx+tanx Answered by Harley Weston. 





Radian measure 
20010726 

From Amy: i have to find out what is meant by the radian measure of an angle and compare it to the measure of an angle in degrees. Answered by Harley Weston. 





Three chords 
20010628 

From Paul: AE is a diameter of a circle and AC, CD and DE are chords of lengths 1, 2 and 3 respectively. (See the diagram.) Find the ridius of the circle. Answered by Harley Weston. 





The angles in a triangle 
20010511 

From Nikki: Find the measure, to the nearest degree, of each angle of a triangle with sides of the given lengths. 26, 35, 40 Answered by Penny Nom. 





The unit circle and trigonometry 
20010405 

From Ashley: "My teacher wants us to find out what a unit circle is, which I found out, a circle with the radius of 1, but the problem is he wants us to show the relationship between the unit circle and the sine(30,45,60 degrees), cosine(30,45,60 degrees),and tangent ratios(30,45,60 degrees). I need help with this and my teacher will not help us out. Thanks very much ... Answered by Penny Nom. 





A famous landmark 
20010323 

From Corinne: A family is traveling due west on a road that passes a famous landmark. At a given time the bearing to the landmark is N 62 degrees W, and after the family travels 5 miles farther the bearing is N 38 degrees W. What is the closest the family will come to the landmark while on the road? Answered by Harley Weston. 





The angle of elevation 
20010308 

From Jeffrey: At a Certain time, a vertical pole 3m tall cast a 4m shadow. What is the angle of elevation of the sun? Answered by Harley Weston. 





cot(arcsin 3/5) 
20010107 

From Jason: Find value. Assume that all angles are in Quadrant 1. cot(arcsin 3/5) Answered by Harley Weston. 





Triangles and trigonometry 
20001130 

From Mose: If I have a right triangle, and I know the lengths of all three sides, is there a formula that will allow me to determine the measurements of the 2 non right angles? Answered by Harley Weston. 





Trig identity crisis 
20001129 

From Rhiannon: I have tried many times to find the answer to these problems but I can't I am in grade 12  tan(x)=csc2(x)cot2(x)
 cos(x)/csc(x)2sin(x)=tan(x)/1tan(x)
 cos(x)[ tan^{2}(x)11]/cos^{2}(x)+sin^{2}(x)=sec(x)
Answered by Harley Weston. 





Overlapping a circle and a square 
20001028 

From Jacky: A square with a dimension 20 by 20cm. and a quarter of the circle with the radius of 25cm (A quater of a circle is created by 2 cuts that are perpendicular bisectors of each other where the intersecting point is at the centre of the circle). With these 2 pieces, the 2 pieces are placed over each other in which the 90^{o} angle of the quarter circle matches with one of the right angles on the square. Now, calculate the overlapping area of the 2 figures. Answered by Chris Fisher and Harley Weston. 





Logs and trig functions 
20000912 

From Becky: How do they get these answers?  log 8 + log 2 = ?
Answer is: log 16
 For 0 degree < x < 90 degree, how many solutions are there for the equation 2sin x = cos x?
Answer: 1
Answered by Penny Nom. 





Trigonometry 
20000902 

From david: determine the sum of the angles A,B where 0 <= A , B <= 180 (degrees) sinA + sinB = sqr(3/2) , cosA + cosB = sqr(1/2) Answered by Chris Fisher. 





Some trigonometry 
20000811 

From Angela: I have some PreCal questions. I am a student at the secondary level. I would be very grateful for your help. Solve the equation for theta (0 <= theta < 2pi). tan^{2}(theta) = 3 I know sec^{2}(theta) 1 = tan^{2}(theta) . . . Answered by Harley Weston. 





A semicircle and a triangle 
20000728 

From Ben: A semicircle and an isosceles triangle ABC have the same base AB and the same area. The equal angles in the triangle are BAC and CAB. I have to find the value of each of these angles. Answered by Harley Weston. 





A trig question 
20000701 

From Will: An open rectangular tank a units deep and b units wide holds water and is tilted so that the base BC makes an angle theta with the horizontal. When BC is returned to the horizontal, who that the depth of the water is (a squared) * cot theta div 2b units Answered by Harley Weston. 





Two problems 
20000612 

From Sharon: If f(4)=0 and f(6)=6, which of the following could represent f (x)? A. 2/3x4 B. x+2 C. x4 D. 3/2x+6 E. 3x12 these are problems to study for a test so I need to know the answer and how it was solved! I have one more question If 180^{o} < theta < 270^{o} and tan theta = 4/3, then sin theta =? A. 5/4 B. 4/5 C. 3/5 D. 12/5 E. 3/5 Answered by Harley Weston. 





Projecting a line segment onto a plane 
20000608 

From Monica: What is the measure of the angle determined by a 14 inch segment and its projection into a plane if the length,in inches, of the projection into the plane is 7 inches? Answered by Penny Nom. 





Using the inverse sine function 
20000531 

From Nelson Rothermel: This has me completely baffled. I have to use the laws of sine or cosine to find the angles of a triangle when I have 3 sides, so I can't go 180xy when I have 2 angles. Now, I have a triangle with values of 3, 7, and 9. Here are the steps I used (A,B,C are angles; a,b,c are opposite sides): angle A (16.1951 degrees): cos^{1}*((b^{2}+c^{2}a^{2})/(2*b*c)) angle B (40.6011 degrees): sin^{1}*(b*sin(A)/a) angle C (56.7962 degrees): sin^{1}*(c*sin(A)/a) If you notice, A+B+C does not equal 180. According to the book, A and B are correct, but C is supposed to be 123.2038 degrees. Why doesn't it work??? Answered by Harley Weston. 





A trigonmetric identity 
20000515 

From Caitlin: My name is Caitlin and my question is from 11th grade math and I'm a student my question is I need to solve this identity : cos x csc x  sin x sec x = 2 cot 2x Answered by Paul Betts. 





Solve 2sin 3x1=0 
20000511 

From Cynthia: How would you solve 2sin 3x1=0? I don't know what to do with the 3. Answered by Penny Nom. 





Trig functions 
20000509 

From Melissa: Find all solutions in the interval (0,2pi) 2cos^{2}x3cosx4=0 Answered by Paul Betts and Harley Weston. 





sin(7pi/12) 
20000504 

From Kristel: What is the exact value of sin 7pi/12? Answered by Chris Fisher and Paul Betts. 





A trogonometry problem 
20000312 

From A student: Find all values of X in the interval 0 degrees <= x < 360 degrees that satisfy the equation 2sin x  cos 2x = 0. Answered by Harley Weston. 





Folding a page 
20000301 

From Krista Bischoff: One corner of a page of width a is folded over and just reaches the opposite side. Express L, the length of the crease, in terms of x and a. I can't get the picture to copy to this form so I guess I will have to try and describe the picture the best that I can. The top right hand corner is folded to the left side, almost half way down. The width of the paper is a ( the width of the bottom part which is not folded.) The creased side is L and the part shorter part of the folded area is x (the part that would have been the top right of the original piece.) Answered by Chris Fisher. 





Triple angle formula 
20000223 

From Sara: Can one derive a triple angle formula for sine and cosine? If so, how? Answered by Chris Fisher. 





A trig identiry 
20000223 

From Ashlee: I am having problems doing this problem. Can you help? Verify the identity: (1+cot^{2}X)(1cos2X)=2 Answered by Harley Weston. 





A trig identity 
20000217 

From Eric:
Question: How do I solve this problem? sin3x cos3x _____  _____ = 2 sinx cosx Answered by Chris Fisher. 





Period 
19991228 

From Mahdawi: I have attached a diagram of the graph, and I need to find out its period. I really don't understand how to do so, please help! Answered by Harley Weston. 





Proving a trigonometric identitiy 
19991217 

From Ryan: I need to figure out how to prove that sec^{2}x + csc^{2}x = sec^{2}x csc^{2}x. I am not sure where to start out with it and whether I should use reciprocal, quotient, or pythagorean. Answered by Penny Nom. 





Sines & cosine laws 
19991210 

From Pierre Boivin: Triangle LMN, angle L=71 degree , LM= 7.2 , MN=8.3 , ln= 5.9 The questiion was to find angle M. Using the cosine law I found the answer to be 44 degree. It is also the book answer. Using the sines law I found the answer to be 42.2 degree. why can't I use the sines law. Answered by Chris Fisher. 





Cos x = 1/2 
19991201 

From Pierre Boivin: When I factor[ 2cos (square)  5cos 3], I get (2cos + 1)(cos  3). 2cos + 1 = 0, 2cos = 1, cos = 0.5,. Using inv cos on calculator, I get 120 degree related angle. When I graph I get two values, between 90 and 180 degree and between 180 and 270 degrees. How do I find those two values. How do use 120 degree in relation with the x axis. Answered by Penny Nom. 





Women in Trig 
19991011 

From Sandra Mills: I am looking for some information about women who have contributed to the discipline of trigonometry. In addition to this I have been asked to choose a subject pertaining to Roman times for my Roman and American Lit class. I wanted to do a project and presentation related to mathematics, but could use some suggestions maybe how mathematics were applied as in engineering and the structure of the Roman buildings. Could you please provide some information about the history of mathematics and it's applications in Roman times. I am also open to any other suggestions for topics. Answered by Chris Fisher. 





sin x = x/10 
19991007 

From Amandeep Grover: Solve the equation sin x = x/10 Answered by Harley Weston. 





A trig limit 
19991006 

From Yannick Gigandet: What is the limit, as x approaches pi/3, of (12cosx) / sin(x(pi/3)) ? Answered by Penny Nom. 





Two limits 
19991002 

From Jennifer: How do I find lim (1cosx)/(x^2) as x> 0 and lim (tan3x)/x as x>0 Answered by Harley Weston. 





Trigonometry history 
19990925 

From Nikki: What is trigonmetry ? Who invented it ? What is it's purpose ? And anything else that you can tell me that is related to Trigometry. Answered by Chris Fisher. 





Distance between the windows 
19990919 

From Lawrence: An observer on level ground is at distance d from a building. The angles of elevation to the bottom of the windows on the second and third floors are a and b respectively. Find the distance h between the bottoms of the windows in terms of a b and d Answered by Harley Weston. 





Degrees and triangles 
19990909 

From Sandra Mills: Are there any triangles which are not 180 degrees? I am also in need of information on the history of degree measure for an angle. Answered by Walter Whiteley. 





A Trigonometry Question 
19990828 

From Diane Simms: My question is can the following be factored. I am a teacher who needs the factors to this right away. 2 Sin^{2}X + 2 SinX CosX  1= 0 Answered by Harley Weston. 





From an airport control tower 
19990804 

From Pammy: Hi I am a 30 yo mature age student doing my HSC but am having difficulty understanding this, if you can help me. From an airport control tower, a Cessna bears 023 degrees T and is 27km away. At the same time, a Boeing 767 bears 051 degrees T and is 61km from the tower. Both planes are at the same height. i) What is the size of angle ATB? ii) Using the cosine rule to calculate the distance the planes are apart, to nearest kilometre. I figured out and drew the triangular diagram but can't figure out the rest and which formula to use. sorry about this, thankyou kindly Answered by Harley Weston. 





Sin 4A 
19990622 

From Ryan Cochrane: If sinA = 4/5, and A is a first quadrant angle, find sin4A Answered by Harley Weston. 





A trig problem 
19990603 

From Stu Barnes: cos(theta) / 1+ sin(theta)=sec(theta)tan(theta) I've being having trouble with this one on my correspondance course. Answered by Harley Weston. 





Dig digs in the garden 
19990211 

From Katherine Shaw: A circular garden has an a radius of 8m. Dig, the dog, is tied up to a fence that runs round the outside of the garden. Dig was able to dig up all the garden, apart from an area of 64 square metres, which he couldn't reach. How long was his lead? Answered by Chris Fisher and Harley Weston. 





A trig limit 
19981114 

From Amy Atwell: what is the limit of of tanx / x + sin x as x approaches 0 Answered by Harley Weston. 





A Calculus Problem 
19980628 

From Lorraine: I'm a postsecondary student taking calculus by correspondence. I'm stuck on the following question (and similar ones) Can you help? Evaluate the following indefinite integral: d(theta)  1 + sin (theta) (It says to multiply both numerator and denominator by: 1  sin(theta) Thanks Lorraine Answered by Harley Weston. 





A trig limit 
19980528 

From Ann: This problem is a calculus 1 limit problemhigh school level. I'm teaching myself calc over the summer and I'm already stumped. find the limit lim sec^(2)[(sqrt2)(p)]1 p>0  1sec^(2)[(sqrt3)(p)] I'm Ann. Answered by Harley Weston. 





Trigonometry history 
19980526 

From Joeseph Huckler: Can you please tell me some history of the trigonometric ratio Tangent? who discovered it? when was it discovered and some other useful info... Answered by Penny Nom. 





Trigonometric functions 
19971221 

From Calvin Cheng: My name is Calvin and I have a year 12 question for you to help me with. From a point S, the angle of elevation of the top of a tower due north of it is 20 degrees. From R, due east of the tower, the angle of elevation is 18 degrees. S and R are 100m apart. Find the height of the tower. Answered by Harley Weston. 





Cos(x) Cos(2x) Cos(4x)=1/8 
19970924 

From Tan Wang: How many distinct acute angles x are there for which cosx cos2x cos4x=1/8? Answered by Chris Fisher Harley Weston and Haragauri Gupta. 





A Trigonometric Limit 
19970918 

From Brian Ray: What is the limit, as x approaches 0, or tan^23x/x^2? (read, tan squared 3x over...)? Answered by Harley Weston. 





Finding the Mine 
19970623 

From Billy Law: Tom is gold prospector. On his last trip out from town, he headed 35 degree South of West to a lake where he had lunch. The lake was 24 km out of Town. He then headed due East for 35 km before Doubling back on bearing of 15 degree South of west for 20 km to reach his mine. By converting to Cartesian coordinate before doing vector additions do the following: a) Calculate the position of the mine from town in term of a distance and a direction. ... Answered by Harley Weston. 





A problem with arccos. 
19970609 

From Vanessa Chan: Prove: arc cos4/5 + arc cos (5/13) = arc cos (56/65) Answered by Harley Weston. 





Solving a Trig Equation. 
19970428 

From Susan Harvey: Hi I am a teacher and have a calculus problem that I have a solution to but it seems so involved that I would be interested to see if their were other solutions. Solve for x, if x is from 90 to 90 degrees tan2x = 8cos{squared}x  cotx Answered by Chris Fisher Denis Hanson and Harley Weston. 





A trig problem 
19961213 

From S. Johnson: sin t + cos t = 1/5. Find ALL exact values of cot t, given the original equation. Answered by Harley Weston. 





Trigonometry 
19961112 

From Evans: Any idea who came up with some or most of the ideas involved in trigonometry? Answered by Chris Fisher. 





Height of a Hotel 
19961107 

From Irene: "Irene" is to determine the # of floors in a hotel 500 feet up the street. Irene is on the 10th floor of an office building and can measure the angle of elevation to the top of the hotel, 57 degrees. Her view of the entire building is obstructed. If the street rises at an angle of 8 degrees from the office building to the hotel and the average distance between floors is 11 feet, how many floors are on the hotel? Answered by Penny Nom. 





The diameter of the sun. 
19961029 

From Lynda Mow: What is the process for solving the following question? As viewed from earth, the sun subtends an angle of approx 32'. If the sun is 93,000,000 miles from earth, find the diameter of the sun. Answered by Penny Nom. 





A trig identity 
19960311 

From Azmat Hussain: Is there an easier/another way to prove the trig identity cos(a+b) = cos(a)cos(b)sin(a)sin(b)? Answered by Penny Nom. 





Trig identities 
19951130 

From Azmat: Why do we work on the two sides of a trig identity separately? Answered by Harley Weston. 





Trigonometrie 
20090807 

From Michaël: Bonjour,
Je cherche a vérifié cette relation de trigo,
Tan^2x = Sin^2x +Sin^2x*Tan^2x.
après de nombreux essais, j'arrive à ce résultat:
Tan^2= 1cos^2x + 1cos^2x*(sin^2x/cos^2x)
Merci de votre aide Answered by Claude Tardif. 





exercice de trigonométrie 
20080219 

From Maxime: Montrer que dans un triangle quelconque le produit des cosinus des angles
cosA*cosB*cosC est inférieur ou égal à 1/8. Answered by PierreLouis Gagnon et Thierry Moisan. 





cos^3x+sin^3x=1 
20070607 

From sannier: bonjour je bloque sur l'equation: cos^3x+sin^3x=1
j'ai essayé toute les formules de trigonometrie je n'y arrive pas.connaissez vous un moyen de resoudre cette equation ou de m'orienter? Answered by Claude Tardif. 





problème de trigonométrie 
20051101 

From Manon: Soit un triangle ABC, de cotes a , b et c, avec A=45° et B=60°.
Apres avoir demontre que 3a²2b²=0 (que jai fais en utilisant la regle du sinus) et a²2c²+2ac=0 (que jai fait en utilisant la regle du cosinus), vous montrerez que laire du triangle ABC peut sexprimer: { [ 3 + racine carre 3 ] / 12 } b² unites.
Je ne sais pas comment arriver a cette expression de laire. Je narrive pas a exprimer c² et ac en fonction de b².. et je pense que ca pourrait vraiment aider..
puisque je suis arrive a letape:
ac[(racine carre 3) / 4]
avec ac = a² + c²  b²
et a² = 2/3 b²
ms c²= 1/3 b² + ac Answered by Claude Tardif. 





Des tables trigonométriques 
20031120 

From JeanJacques:
Je suis à la retraite et en train de mettre à jour mes connaissances en trigonométrie. On peut facilement trouver les rapports entre les côtés d'un triangle droit ayant des angles secondaires de 30, 45 et 60 degrés, mais comment s'y prendon pour calculer les rapports entre les côtés d'un triangle droit ayant des angles secondaires de valeurs intermdiaires. En d'autre mot, comment s'y prendon pour faire le calcul détaillé des tables trigonométriques. J'ai cherché en vain dans divers textes de géométrie la réponse à cette question. Merci à l'avance pour l'attention que vous porterez à ma requête. Answered by Claude Tardif. 





Un peu de trigonométrie 
20021216 

From Hubert: J'ai 37 ans et les mathématiques sont relativement loin dans ma mémoire, je voudrais savoir s'il existe un méthode pour résoudre une équation du type. a1*cos(x) + a2*sin(x) + a3*cos(2x) + a4*sin(2x) + a5 = 0 Answered by Claude Tardif. 





Question de trigonométrie 
19971211 

From JeanPierre Quesnel: Je suis dans le désert et je parcours 1000 km à partir du point "A" jusqu'au point "B". Si je reviens au point "A" et fais une rotation de 8 degrés en faisant un autre 1000 km, quelle sera la distance en km entre les points "B" et "C". Answered by Diane Hanson et Penny Nom. 

