







Solve the equation completely cos 2x = 1 
20170608 

From Lava: Solve the equation completely cos 2x = 1 Answered by Penny Nom. 





How far apart are the boats? 
20161213 

From Halley: Two boats leave port at the same time. Boat A travels east at a speed of 12 km/hr. Boat B travels southwest at a speed of 14 km/hr. After two hours, how far apart are the boats? North is 0 degrees. How do I figure this out.
Thanks Answered by Penny Nom. 





Two airplanes 
20150414 

From john: two planes leave an airport at the same time, one going northwest (N35*W)at 400 mph and the other going east at 332 mph. How far apart are the planes after 4 hours to the nearest mile? Answered by Penny Nom. 





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. 





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. 





The sides of a triangle 
20140406 

From Michael: I am supposed to sove for the length of side "b" of an irregular triangle. I am given the following:
Side a: 65'
Side b: Find this length
Side c: 50'
Angle A: unknown
Angle B: unknown
Angle C: 52 degrees
I am supposed to use the law of cosines to solve for side "b" and my teacher
says there is no mistake in the "givens" for the problem. I do not see how
this can be done using the law of cosines and i have not figured out how to sove for
angle B to use the law of cosines. Answered by Penny Nom. 





25% profit 
20140102 

From Finn: Hello,
The question is all about buyandsell business.
Problem:
Pencil  $6 for whole sale price
$8 if I sell the item
How do I get the 25% profit? (you can change the whole sale price and the retail price[if i sell the item])
if I buy the pencil at 24 pieces and sell it at 24 pieces. Answered by Penny Nom. 





Proportional rates 
20131010 

From Varsha: A province's Ministry of Social services has found that both the number of people needing social assistance and the province's total expenditures on social assistance are proportional to the rate of unemployment. Last August when the provincial unemployment rate was 8.4 %, the province provided assistance to 89,300 individuals at a total cost of 4107.4 million. The forecast unemployment rate for next August is 7.9%. How many people can the province expect to need social assistance next August? What amount should the province budget for social assistance in August? Answered by Penny Nom. 





A triangle problem 
20131002 

From raneem: ABC is a triangle in which : BC=20cm. M(<B) =29 and m(<C)=73 . D is the midpoint of BC
Find the length Of AB and AD approximated to 2 decimal places 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. 





We can't write sinx and cosx as a finite polynomial. 
20130331 

From rimoshika: prove that we can't write sinx and cosx as a finite polynomial. Answered by Walter Whiteley. 





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. 





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. 





Integral 1/(25x^2)^3/2 
20120222 

From John: Integral 1/(25x^2)^3/2 Answered by Harley Weston. 





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. 





Three sides of a triangle 
20111224 

From saba: the three sides of a triangular lot have lengths 10,11and 13cm,respectively.
find the measure of its largest angle and the area of the lot? 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. 





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 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. 





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 quadrilateral with 4 known sides and 1 known angle 
20100319 

From samuel: Name: Samuel
Status: Student
I have a quadrilateral with 4 known sides and 1 known angle, and I'm trying to evaluate the other angles of my quadrilateral.
By the law of cosines, I can easily find my opposite angle (using the diagonal as a basis for the equation).
However, to find the two remaining angles, I have found no other way so far than to use the other diagonal, which can be found with the equation attached (from geometry atlas).
Is there any simpler way? Answered by Robert Dawson and Harley Weston. 





Solving a triangle 
20100125 

From Paige: how do i solve a triangle with one angle of 73 degrees,
one angle of 32 degrees, and one side of 23cm? 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. 





How fast is the distance between the two cars decreasing? 
20091208 

From Jenny: Two cares are on a collision course toward point P. The paths of the two cars make a 30 degree angle with each other. The first car is 40 km from P, and traveling toward P at 16 km/hour. The second car is 50 km from P, traveling at 20 km/hour. How fast is the (straight line) distance between the two cars decreasing. (Hint: Law of Cosines) Answered by Harley Weston. 





Three angles and one side of a triangle 
20091116 

From Esther: How do i find the sides of an acute triangle if i know the angels are 60,45,75 and i only know one side which is 10? Thanks! Answered by Penny Nom. 





Vectors and the Law of Cosine 
20090608 

From lauren: once 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 Janice Cotcher. 





Related rates 
20090309 

From Megan: A plane flying with a constant speed of 330 km/h passes over a ground radar station at an altitude of 3 km and climbs at an angle of 30°. At what rate is the distance from the plane to the radar station increasing a minute later? Answered by Harley Weston. 





Find the resultant of this displacement pair 
20090222 

From katydidit: Find the resultant of this displacement pair:
500 miles at 75 degrees east of north and
1500 miles at 20 degrees west of south.
How do I graph this and how do I solve this problem? Answered by Penny Nom. 





The angle between two lines 
20081217 

From abhi: how to calculate the angle between two lines, given the length of the lines..
angle should vary from 0  360 in the counterclockwise direction Answered by Robert Dawson and Harley Weston. 





The path of a small sailboat 
20081119 

From jane: a sailor in a small sailboat encounters shifting winds. she sails 2.00 km East
then 3.40 km North East, then an additional distance in an unknown direction. Her final position
is 6.68 km directly east of the starting point. find the magnitude & direction
of the third leg of the voyage. 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. 





The angles and sides of a triangle 
20081113 

From JAMIE: a triangle with a side(b)37m an angle(C)70degrees and (a)79m find values of angles A and B and length of side c Answered by Stephen La Rocque. 





Radii and Chords Create a NonRight Triangle 
20080822 

From Beary: AOC is a diameter of circle O. Line AB is 12, and lines OA and OC (the radii) are 10. Find the length of line BO and chord BC. Answered by Janice Cotcher. 





Angular & Linear Speed from a Sine Graph 
20080819 

From Kim: Kim, a student:
I am given a graph with a wave. The amplitude is 5cm and the period is 4cm. I am suppose to find the angular speed. What I need to know is the formula for angular speed and how do I use these numbers to get the correct answer. Answered by Janice Cotcher. 





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. 





Arclength and sectorangle 
20080806 

From Benson: If chord length, radius are given, How to find the sector angle and arclength Answered by Janice Cotcher. 





Trigonometric 
20080728 

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





Guy wires for a tower 
20080519 

From larissa: a radio tower 500 feet high is located on the side of a hill ( the hill has an inclination to the horizontal of 5 degrees.) How long should two guy wires be if they are connected to the top of the tower and are secured at two points 100 feet directly above ( up the hill ) and directly below the base of the tower? Answered by Penny Nom. 





The length of the third side of a triangle 
20080216 

From mary: I have an angle of 72 degrees and each of the sides are 5' long. What is the distance from each of the ends of the 5 feet to form a triangle. 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. 





The angles of a triangle given the three sides 
20080117 

From Lucy: Is there a way to find the angles of a triangle just by knowing the lengths of it's sides?
It seems like the would be a relationship between the two, but I'm not sure. Answered by Stephen La Rocque and 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. 





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. 





Ramp height 
20071203 

From Steve: I need to find the height of a angle.
23 degree angle at 12 feet of length is how high from the ground? Answered by Stephen La Rocque. 





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. 





Area of a quadrilateral 
20071010 

From Courtney: how would i find the area of a quadrilateral..
the sides are a (/) is 6cm, b (—) is 9 cm, and c (\) is 7 cm..
the angle between a and b is 140 degrees and b and c is 115 degrees.. Answered by Stephen La Rocque. 





The length of the third side of a triangle 
20070815 

From Brooklyn: What is the equation to find the length of the third side of a triangle if you have the length of A, B, and the angles(s)? Answered by Stephen La Rocque. 





The swaying of a building in the wind 
20070811 

From San: During a strong wind, a tall builing, such as the CN Tower, can sway
back and forth as much as 100cm, with a period of 10 seconds.
Please help me to determine the equation for this function, in the form
y=asinkx Answered by Stephen La Rocque. 





Calculating the area (acreage) of a four sided lot 
20070718 

From A property owner: I have a real estate property and the lot size is something I need to find out. I know the lengths of the four sides, but it isn't a rectangle, it is an odd shape. How do I find the acreage? Answered by Stephen La Rocque. 





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. 





Any regular polygon inscribed in a circle 
20070712 

From DJ: Circle with r=12" is inscribed in a regular octagon. What is the length of each octagon segment?
Note: Our answer works for any regular polygon inscribed in any circle. Answered by Stephen La Rocque. 





sinx and cosx 
20070625 

From Mac: Can anyone tell me whether sinx and cosx is differentiable at x=0 ?
As far as i know, cos(x) and sin(x) is differentiable at all x. Answered by Penny Nom and Stephen La Rocque. 





Angles of depression 
20070613 

From Phonda: The pilot of a small private plane can look forward and see the control tower for a small airstrip. Beyond that is a large factory that is 3 milies from the airstrip. The angles of depression are 12.5 degrees and 4.8 degrees respectively.
Find the airplane's altitude, to the nearest ten feet. 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. 





The area of a quadrilateral 
20070610 

From Lucy: Calculate the area of the quadrilateral ABCD.
AB= 4.1cm, BC = 7.6cm, AD= 5.4 cm, CD= ?
Angle ABC = 117, Angle ADC = 62.
Give your answer correct to 3 significant figures. Answered by Stephen La Rocque and Penny Nom. 





The law of sines 
20070609 

From Felicia: A parallelogram has one side that is 12.0 cm and one angle that is 65°. The shorter diagonal is 25.0 cm. To the nearest tenth of a centimetre, how long is the other side of the parallelogram? Use the sine law. Answered by Penny Nom. 





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. 





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. 





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. 





The law of cosines 
20070323 

From chetna: Q 1) In triangle LMN, l=7, m=5 , n=4. find ANGLE N.
After applying the rule and substituting values i'm getting
Cos n= 58/40. Is there something wrong. The answer at the back of the book is 34 degrees. Answered by Penny Nom. 





A curve on a cylinder 
20070127 

From John: think of a tube,say 50mm in diameter made out of cardboard, project vertical lines at right angles from the base at say every 2mm right round the tube in pencil.No pretend you can put this cardboard tube in a saw and cut it at 45degrees. Get a pair of scissors and cut it at the lowest end and lay it out flat.It now looks like a graph,how do you work out each of these vertical lengths possibly chord lengths Answered by Stephen La Rocque and Penny Nom. 





lim x>infinity cos x 
20061207 

From Katie: I was wondering if it was possible to find: lim x>infinity cos x Answered by Stephen 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. 





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 chord length of a polygon 
20060614 

From Krishna: I have to find out the chord length of a polygon  Tetradecagon ! The Radius of the Circle is 11.5 Cms. The Circle is intersepted by 14 arcs. Then how to find out the chord length? Answered by Stephen La Rocque. 





The interior angles of a right triangle 
20060520 

From Greg: I am wondering if there is a way to figure out the interior angles of a right triangle if we know ONLY the side lengths, and the trick is, we CANNOT use arctangent! Answered by Leeanne Boehm and Penny Nom. 





Given three angles and a side 
20060409 

From Jon: How do you figure out the length of all sides of a scalene triangle if given the measure of all angles, and one side? 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. 





Three towns are located at the vertices of an equilateral triangle 
20060320 

From A student: three towns are located at the vertices of an equilateral triangle. The towns are 8, 5, and 3 miles, respectively, from a store. How far apart are the towns? Answered by Chris Fisher. 





sinh(i/2) 
20060209 

From Louis: How can you set up an equation to find sinh(i/2) Answered by Penny Nom. 





How do you find the angles in a triangle? 
20060127 

From Keith: How do you find the angles in a triangle if you know the lengths of the sides? Answered by Chris Fisher and 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. 





The period of sin(x) + cos(x) 
20050721 

From A student: WHAT IS THE PERIOD OF SIN(X)+COS(X)? Answered by Penny Nom. 





Angle of incline 
20050515 

From Kyle: What is the degree of incline of a 12 foot plank that goes from 10.5 inches on one end to zero inches on the other? Answered by Penny Nom. 





The length of a chord 
20050113 

From A parent: Does anyone have a formula for calculating the chord length for a segment of a circle when you know the radius and the enclosed angle or radian ? 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. 





Solving triangles 
20041030 

From Allen: Solve the following triangles.
Given
1. B = 20 Degrees, a = 25, b = 16
2. A = 35 Degrees, b = 2, c = 3
3. A = 32 Degrees, C = 44, c = 20 Answered by Harley Weston. 





sin(3A) 
20041020 

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





The law of sines 
20040801 

From Joy: How do you solve this? Do you solve this triangle using the law of sines of the law of cosines? (ASA)
A=120DEG. B=40DEG c=35 cm
I keep getting different answers. Answered by Penny Nom. 





Finding bearings 
20040524 

From James: This question is about finding bearings. A boat race starts from point A, goes North to Point B, a distance of 1000 meters. The course is triangular. The bearing from point B to point C is South 70degrees West. The distance from Point B to point C is 1500 meters. Find the course bearing from C to A.
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. 





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. 





Business trip 
20031219 

From Ameer: A businnessman drives from Washington, D.C., to Boston, a distance
of 442 miles, and then makes the return trip. On the way to Boston,
he drives 65 miles per hour, taking an 1hour rest stop during the
drive. After finishing his business in Boston, he make the return
trip driving at 60 miles per hour and takes a 45minute rest stop
halfway through the trip. Which leg of the journey, Washington, D.C.
to Boston, or Boston to Washington, D.C., takes the longer time? 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. 





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. 





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. 





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. 





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. 





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. 





Adding vectors 
20020112 

From Lena: how do you add vectors together? If you are given the length and angles of both vectors and are asked to add/subtract them, how do you do it? I know you are supposed to do the head to tail method, but whenever i try it i get the wrong answer. I need help setting it up. example: A is 2.7cm, and 60 degrees, B is 1.6cm and 135 degrees, find the magnitude and amplitude Answered by Penny Nom. 





The tangent function 
20020112 

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





A trig identity 
20010727 

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





The speed of the boat 
20010712 

From Sharon: A motor boat is travelling in a southeasterly direction in water that is flowing from the south at 2km per hour. Show that the speed of the boat is (6 times the square root of 2) km per hour, given that it can travel at 10km per hour in still water. Answered by Penny Nom. 





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 law of cosines in the real world 
20010221 

From Hope: Do you have any examles and/or labs that show how the law of cosines is used in the real world? Answered by Harley Weston. 





Law of cosines 
20010220 

From Emily: I missed a few days of class and I can't figure out how to solve Law of Cosines problems. I have the notes and formulas but I can't figure out how to do the math involved to answer the problems. I am also getting confused about how to use degrees and seconds in the Law of Sine and Cosine. I can't seem to get the correct answers and I don't really know how to solve them and enter them into my TI 86. 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. 





The laws of sines and cosines 
20010102 

From Faydene: Can the sine /cosine rule be applied to a right angle triangle to find a particular solution or are these 'rules' applied only when the triangle is not right angled? Answered by Penny Nom. 





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. 





Vector Problem 
20001127 

From Ben: An aircraft can fly 260km/h in still air and the wind is blowing at 70km/h towards the West. In what direction should the aircraft head so that its actual velocity is on a bearing of 030 degrees? Answered by Harley Weston. 





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. 





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. 





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. 





sin(7pi/12) 
20000504 

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





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 identity 
20000217 

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





Graph of a sine function 
19991223 

From Pierre: Given; amplitute:1 period: 540 Phase shift: 60 degree,right I am ask to right the equation: sin 2/3 (value 60degree) When I am asked to graph the equation, the period is mixing me up. Answered by Harley Weston. 





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. 





sin x = x/10 
19991007 

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





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. 





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. 





Ajax, Beverley, Canton and Dilltown 
19970314 

From S. Johnson: The following towns are placed on a coordinate system. Ajax at (x,z), Dilltown at (10,0), Canton at (0,0) and Beverly at (0,10). The roads from Beverly to Canton and from Canton to Dilltown are perpendiculat to each other and are each 10 miles in length. A car traveling at all times at a constant rate, would take 30 minutes to travel straight from Ajax to Canton, 35 minutes to travel from Ajax to Canton via Beverly, and 40 minutes to travel from Ajax to Canton via Dilltown. What is the constant rate of the car, to the nearest tenth of a mile per hour. Answered by Chris Fisher 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. 





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. 





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. 





probleme sin cos 
20060219 

From Thibault: mon probleme commence par: f(x)=sinx (sinx+1)+ cos²x
donc en le dévellopant on trouve: f(x)= sin²x + sinx + cos²x
et apres ce que je ne comprend pas est que par la suite on trouve: f(x)= 1+sinx
qu'estce qui fait que l'on trouve ce resultat?? Answered by Claude Tardif. 

