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A triangular garden 2020-05-24
From yoonji:
the 3 sides of a triangular garden measure 200 ft., 250 ft., and 300 ft., respectively. the garden is to be divided by a line bisecting the longest side and drawn from the opposite vertex. what is the length of the bisecting line?
An angle i a triangle 2020-05-16
From Ogunjobi:
Two goal post are 8m apart a footballer is 34 m from one post and 38m from the other within what angle must he kick the ball if he is to score
The missing diameter of a truncated cone 2020-04-17
From Brandon:
Need a formula to find missing large Dia of a truncated cone where the small dia =.19" Height= 2" and taper =16deg
From Elena:
After 9 weeks Mikayla has an average ark of 5 out of 10 in the weekly spelling tests. What is the minimum number of extra weeks now required to raise her average to 7?
400 in 7.5 billion 2019-08-28
From Emma:
What is a better way to express 400 in 7.5 billion? My daughter has a rare condition, I want to know the answer to say “she is 1 in a ...”
Solve sinX=0.703X for X 2018-03-13
From PARAM:
sinX=0.703X
0.366 x cos square (02 degree 17 mins 27 seconds) 2018-03-12
From michael:
what is 0.366 x cos square (02 degree 17 mins 27 seconds)
what is 0.366 x cos square (88 degree 26 mins 45 seconds)

A footballer angle 2018-02-14
From Kim:
Two goal posts are 8m apart. A footballer is 34m from one post and 38m from the other. Within what angle must he kick the ball if he is to score a goal.
Solve the equation completely cos 2x = 1 2017-06-08
From Lava:
Solve the equation completely cos 2x = 1
How far apart are the boats? 2016-12-13
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
How can I express Sin 4A in term of Sin A? 2016-02-22
From Odukoya:
How can I express Sin 4A in term of Sin A?
1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 x 0 + 1 = ? 2015-06-18
From Sharon:
1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 x 0 + 1 = ?

I got 1 as my answer despite BODMAS making it 12 because logic tells me I ought to place brackets around the first set of repeated addition. Could you please clarify this for me? Thank you 😊

Two airplanes 2015-04-14
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?
Some non-decreasing sequences 2015-04-13
From Sky:
Hi I'm a Student and i'll try my best to state the problem perfectly.

The number of non-decreasing sequences of size at least 1 and at most N, such that each element of the sequence lies between L and R, both inclusive.

Eg:- N=1 L=4 R=5
ans= 2. [{4},{5}]

N=3 L=4 R=6
ans= 19. [{4},{5},{6},{4,4},{4,5},{4,6},{5,5},{5,6},{6,6} {4,4,4},{4,4,5},{4,4,6},{4,5,5},{4,5,6},{4,6,6},{5,5,5},{5,5,6},{5,6,6} ,{6,6,6}]

sin x = cos x 2015-01-23
From Mubashir:
there are two curves y=sinx and y=cosx intersecting at point where x is less than 90 and greater than 0.to find the point I made a equation sinx=cosx but donot know what to do further .please help me by solving this equation sinx=cosx also tell me that have you solved this equation by reference to the graph or by other means please do elaborate your solution in your answer.
Missing digits in a phone number 2015-01-07
From Janelle:
I had a friend try and play a game on me, regarding phone numbers, so I only know the area code , and the last four digits of the phone number. Which means, there are 3 digits that I need to figure out all the possibilities to.
Trig functions and the unit circle 2014-10-02
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.
Solve sin3x = cos2x 2014-07-14
From Emanuel:
If sin3x=cos2x, find the value of x when x<0<90'
A triangular chicken pen 2014-04-27
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!

The derivative of sin(x) 2014-04-26
From Lucky:
f(x)=Sin(x), by first principle its f'(x)...show me how to solve such problem.
The sides of a triangle 2014-04-06
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.

25% profit 2014-01-02
From Finn:
Hello,
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.

Proportional rates 2013-10-10
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?
A triangle problem 2013-10-02
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
A sequence or a series? 2013-09-05
From Rahul:
Whether the following sequence is increasing or decreasing? I even do not kow whether to call it a sequence or not. an = (1/(1+n))+(1/(2+n))+....+(1/(n+n)). I am confused. It looks like a series to me. Please help.
Regards,
Rahul

siin (A) and sin (A/2) 2013-05-09
From shanaia:
given that sin A=4/5 and A is obtuse.find sin (A/2)
How do i reverse this formula? 2013-04-20
From MK:
I have 22,000,000 worth of gold and wants to want to resell the gold back with a profit. Each transaction of gold will have a transaction fee of 15%, so if i resell the gold back at 22,000,000, I will only get back 18,700,000 after 15% transaction cut. The current formula is X-15%X = Y where X = 22,000,000 and Y = 18,700,000 Will u be able to come up with a new formula if we don't know the value of X but we know the value of Y
Something like this X-15%X = 22,000,000. How do i reverse this formula to find the value of X
Thanks

We can't write sinx and cosx as a finite polynomial. 2013-03-31
From rimoshika:
prove that we can't write sinx and cosx as a finite polynomial.
The fourth side of an irregular polygon 2013-02-01
From Emran:
I have a irregular polygon. I know 3 of the 4 sides, and 2 of the angles. A-B is 285, B-C is 149, and C-D is 310. Angle B is 135 degrees. and Angle C is 45 degrees. Is there a formula to solve for the final side? Thanks.
cos(theta/30) = 1 2012-05-14
From Hope:
cos (theta / 30 = 1
I am very confused as to how to solve it. Can you help?

Integral 1/(25-x^2)^3/2 2012-02-22
From John:
Integral 1/(25-x^2)^3/2
Tangent of theta 2012-01-17
From stahl:
explain what the 'tangent of theta' means. Draw and label a diagram to help with your explanation.
Three sides of a triangle 2011-12-24
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?
58 choose 4 2011-08-26
From Jean:
Using only the numbers 1-59, how many times would the number 23 appear in combinations of 5 numbers?
... Can a list be provided as well?
Thank you very much,
Jean

Decreasing numbers 2011-04-13
A number is called a "decreasing number" if each digit in the number is less than the digit to its left. For example, 87420 is a deceasing number. How many five-digit decreasing numbers are there?
sin x = -0.25 2011-03-29
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

Reversing the digits 2011-02-08
From rejie:
if the digits are reverse , the number is 9 less than the original number.what is the equation?
Sales as a function of advertising 2010-12-08
The sales S(in thousands if units) of a product after x hundred dollars is spent on advertising is given by S=10(1-e^kx). Find S as a function of x if 2500 units are sold when \$500 is spent on advertising.
How far must the pitcher travel to get to the ball? 2010-11-04
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.
A building and a flag pole 2010-09-09
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
Math in the workplace: nursing 2010-05-24
From Taylor:
How is math used in the workplace - Nurse Anesthetist?
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?
A quadrilateral with 4 known sides and 1 known angle 2010-03-19
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.
A sequence 2010-02-07
From Shalev:
hi,

i had a job interview yesterday. it had mathematical questions. couldn't solve 1. i m obsessed with it. please find out what the answer is..

it goes like this: 2,4,5,5,8,6,_,_,14,8

thank u very much

Solving a triangle 2010-01-25
From Paige:
how do i solve a triangle with one angle of 73 degrees, one angle of 32 degrees, and one side of 23cm?
A sequence 2010-01-22
From brahmaji:
0 7 26 63 _ 215 342 fill the blank? find the missing number
A trig question 2009-12-15
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

A telephone pole on a slope 2009-12-14
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.
How fast is the distance between the two cars decreasing? 2009-12-08
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)
Three angles and one side of a triangle 2009-11-16
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!
A sequence 2009-09-19
From Oliver:
I am struggling to work out the missing terms in the following sequence:

1, 3, _, 7, 11, 18, _

Vectors and the Law of Cosine 2009-06-08
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
Related rates 2009-03-09
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?
Find the resultant of this displacement pair 2009-02-22
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?

limit sinx/x 2009-01-30
From Jackie:
how to evaluate limit sinx/x as x tends to zero if x is in degrees
Answered by Stephen La Rocque and Harley Weston.
The angle between two lines 2008-12-17
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 2008-11-19
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.
How far are the boats apart? 2008-11-14
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?
The angles and sides of a triangle 2008-11-13
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
Math and nursing 2008-11-10
From alina:
how many math do you net for nurse
Radii and Chords Create a Non-Right Triangle 2008-08-22
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.
Angular & Linear Speed from a Sine Graph 2008-08-19
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.
Solving for Shared Height of Two Right Triangles 2008-08-17
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.
Arc-length and sector-angle 2008-08-06
From Benson:
If chord length, radius are given, How to find the sector angle and arc-length
Trigonometric 2008-07-28
From kiran:
In triangle , Sin@ = ?
Choosing 4 numbers from 70 numbers 2008-07-21
From Jeannine:
When using numbers from 1 to 70 in sets of 4, how many combinations are there without having the same combination twice? Thanks
Guy wires for a tower 2008-05-19
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?
The limit of (sin4x)/(tan9x) as x approaches zero 2008-03-14
From stev:
as x->0. How do you find the limit of f(x)=(sin4x)/(tan9X)
Moving grain across the river 2008-03-12
From Janice:
Wesley needs to move 820 kg of grain across the river in a canoe that can carry no more than 120 kg. Wesley has a mass of 70 kg. What is the fewest number of trips he will have to make? A. 17 trips; B. 18 trips; C. 32 trips; D. 33 trips.
The length of the third side of a triangle 2008-02-16
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.
The cosine of an angle 2008-01-21
From Kristine:
Find measure of unknown side cosA=0.5
The angles of a triangle given the three sides 2008-01-17
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 2008-01-14
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.

How far is the jet from the lighthouse? 2008-01-07
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

Ramp height 2007-12-03
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?
The perimeter of Wisconsin 2007-11-26
From Kyle:
I am doing a project and I need to figure out the total perimeter of wisconsin in miles and only know the square miles of Wisconsin which is 65,503 and I need to get that to miles I have no clue how to do this. I've looked all of the computer for answers but got none. Thanks
Answered by Leeanne Boehm and Penny Nom.
A curve sketch 2007-11-22
From Ahson:
Find critical points, determine the monotonicity and concavity and sketch a graph of f(x) with any local maximum, local minimum and inflection points labeled:

1. f(x) = x^4 - x^3 - 3x^2 + 1

The definition of the sine function 2007-11-22
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.???

Increasing and decreasing for functions 2007-11-09
From David:
Direction: Identify the open intervals on which the function is increasing or decreasing.

f(x)=1/(x^2)
f'(x)= -2/(x^3)

i understand how to get up until there, and the undf. is x=0, but now i'm having problem setting up the number table chart. i cant remember how, and where to place the increase and decrease + - the chart, for example <---------0----------> where would the increase and the decrease be place?

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..

The length of the third side of a triangle 2007-08-15
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)?
The swaying of a building in the wind 2007-08-11
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
f(x) = (x^4) - 4x^3 2007-07-22
From Michael:
I'm a student who needs your help. I hope you'll be able to answer my question. Here it is: Given the function f(x)=(x^4)-4x^3, determine the intervals over which the function is increasing, decreasing or constant. Find all zeros of f(x) and indicate any relative minimum and maximum values of the function.
Any help would be appreciated. Thank you for your time.

Calculating the area (acreage) of a four sided lot 2007-07-18
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?
Trig functions for angles not between 0 and 90 degrees 2007-07-16
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?
Any regular polygon inscribed in a circle 2007-07-12
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.
sin|x| and cos|x| 2007-06-25
From Mac:
Can anyone tell me whether sin|x| and cos|x| 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 2007-06-13
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.
How high does the ladder reach? 2007-06-11
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?
The area of a quadrilateral 2007-06-10
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 2007-06-09
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.
Finding the hypotenuse without Pythagorus 2007-05-11
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?
Evaluating sine and cosine 2007-05-06
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...
The distance between two fire towers 2007-03-23
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.
The law of cosines 2007-03-23
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.
A curve on a cylinder 2007-01-27
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 2006-12-07
From Katie:
I was wondering if it was possible to find: lim x-->infinity cos x
cos2x=1 2006-11-21
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 2006-07-07
From Scott:
How to prove arc sin x = arc tan( (x)/√(1-x2))
A trig problem 2006-06-24
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.
The chord length of a polygon 2006-06-14
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?
The interior angles of a right triangle 2006-05-20
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.
8-digits numbers with their digits in decreasing order 2006-05-09
How many 8-digits number are there with their digits in decreasing order
Odd-man out coin tossing and probabilities 2006-04-27
From Kalyan:
When four people toss fair coins, what is the probability that in a given toss there will be one "odd man". That is one person whose coin does not have the same out comes as that of any other members?
Given three angles and a side 2006-04-09
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?
Superimposing images 2006-03-30
From Laurie:
I am a parent and trying to find real world applications for the math strand that includes superimposing one item on another to determine identical. The Alberta strand is match size and shape of figures by superimposing one on top of the other. I am trying to find a way to put this into context for everyday life. Any ideas?
Solve the equation cos x = sin 20 where x is acute. 2006-03-26
From Elle:
Solve the equation cos x = sin 20 where x is acute.
Three towns are located at the vertices of an equilateral triangle 2006-03-20
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?
sinh(i/2) 2006-02-09
From Louis:
How can you set up an equation to find sinh(i/2)
How do you find the angles in a triangle? 2006-01-27
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.
The average of 4 numbers is 5. 2006-01-02
From Sheri:
The average of 4 numbers is 5. I have 3 of the numbers already- 5,8,4,? How do i find out what the last number to give me the average of 5?
sin(kx) = x 2005-10-20
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?
The period of sin(x) + cos(x) 2005-07-21
From A student:
WHAT IS THE PERIOD OF SIN(X)+COS(X)?
The value of n*tan*(180/n) tends to pi 2005-07-11
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 = 5002/ 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?
Angle of incline 2005-05-15
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?
The length of a chord 2005-01-13
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 ?
The tide at a boat dock 2005-01-11
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?

Modelling monthly temperature with a cosine 2004-12-25
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.
Solving triangles 2004-10-30
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

sin(3A) 2004-10-20
From A student:
Express sin3A in terms of sinA and cosA.
Crossing a river 2004-09-09
From Barb:
Nine men and two boys, trekking through the jungle, need to cross a river. They have a small inflatable boat and it's easy enough to row it across the river. The boat, however, can hold no more than one man or the two boys. How can they all get across? (Hint. suppose there was only one man and two boys) Does it make math sense and what would the answer be
Answered by Penny Nom and Claude Tardif.
The law of sines 2004-08-01
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.

Finding bearings 2004-05-24
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.
Cosine of 35 degrees 2004-03-03
From Jason:
How do you find the exact solution to cosine 35 degrees.
Sin(3x), cos(3x) and tan(3x) 2004-01-28
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 cos4x- sin4x is the same as cos2x. Is cos8x-sin8x = cos2x also true? Thank you.s
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 1-hour 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 45-minute 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?
Laws of sines and cosines 2003-11-23
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.
Odd powers of sine and cosine 2003-06-25
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 power-reducing formulas. But for the question I have on my hand, the powers of both sine and cosine are odd: ( sin3x + cos7x ) dx.
Two trig problems 2003-06-10
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!

sin theta = 7/8 2003-05-07
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)
Write sin(3x) in terms of sin(x) 2003-05-05
From A student:
Write sin 2x in terms of sin x
y = 1 - sin(x + 60) 2002-12-10
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.
A coin is tossed 11 times 2002-10-31
From A student:
There are 2 people that are playing a game in which a coin is tossed 11 times. The first player gets a point for a toss of heads. The 2nd player gets a point for a toss of tails. whoever gets 6 points wins. Suppose that so far the first player has 2 points and the second player has 4 points. What is the probability that the first player wins the game?
Answered by Andrei Volodin and Penny Nom.
Tree diagrams 2002-10-12
From Denean:
1. For lunch, students can choose juice or milk; hamburger or pizza; and a banana or apple. How many lunch combinations can the students make?

2. In an experiment, Monty can use paper towels or cloth. He can choose red, green, or yellow food coloring. How many combinations are there?

How far apart are the transmitters? 2002-05-18
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?
The law of cosines and obtuse angles 2002-05-09
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.
A trigonometric identity 2002-03-22
From Debby:
I am stuck on a problem and wondering if you can help?? It is: Prove the following:
sec2(X)+csc2(X) = sec2(X)csc2(X)

sin 2x = cos 3x 2002-02-25
From Allan:
solve:

sin 2x = cos 3x

Primary question: how do you handle the cos 3x?

Answered by Paul Betts and Chris Fisher.
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

The tangent function 2002-01-12
From Justine:
if you know that sin45degress = cos45degrees, how do you know that tan45degrees = 1?
Division symbol 2001-12-12
From Amanda:
What is the name of the symbole used in a long divison problem that seperates the two factors? It looks like a little house.
A trig identity 2001-07-27
From Jeff:
prove this identity and show steps
tan(x/2+pi/4)=secx+tanx

The speed of the boat 2001-07-12
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.
Where is the other \$1? 2001-06-05
From Samantha:
3 people go to a motel. The room is \$30. They split it \$10 each. While in the room the Mgr. tells the clerk the room was only \$25, so he gives her \$5 to take back to the 3 people. On the way she cant decide how to split the \$5 between the three people so she puts \$2 in her pocket and gives them \$1 each.....Therefore, the room now only cost the three people \$9 each, which is \$27 plus the \$2 the clerk pocketed,making a total of \$29.....Where is the other \$1?
The angles in a triangle 2001-05-11
From Nikki:
Find the measure, to the nearest degree, of each angle of a triangle with sides of the given lengths.

26, 35, 40

The unit circle and trigonometry 2001-04-05
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 ...
A famous landmark 2001-03-23
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?
The repetend in repeating decimals 2001-03-21
From Sharon:
What is the name for the bar over the repetend in repeating decimals? Also, what is the name of the long division "house"?
The law of cosines in the real world 2001-02-21
From Hope:
Do you have any examles and/or labs that show how the law of cosines is used in the real world?
Law of cosines 2001-02-20
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.
The "goesinta" box 2001-02-07
From Bridget:
We are looking for the "proper" name of the "box" that is drawn around the dividend on a division problem:

`  ___ 3)12 `

It has always been a family joke to call it the "goesinta" box, but a search of several reference sources hasn't yielded an answer --

This is a question of curiosity rather than a question for homework.

Processing speed 2001-01-26
From Zac:
A COMPUTOR IS ADVERTISED AS HAVING A PROCESSING SPEED OF 11 MILLION INSTRUCTIONS PER SECOND. ON THE AVERAGE, HOW LONG DOSE IT TAKE TO PROCESS ONE INSTRUCTION AT SUCH A SPEED?
cot(arcsin 3/5) 2001-01-07
From Jason:
Find value. Assume that all angles are in Quadrant 1.

cot(arcsin 3/5)

The laws of sines and cosines 2001-01-02
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?
Trig identity crisis 2000-11-29
From Rhiannon:
I have tried many times to find the answer to these problems but I can't I am in grade 12
1. tan(x)=csc2(x)-cot2(x)
2. cos(x)/csc(x)-2sin(x)=tan(x)/1-tan(x)
3. cos(x)[ tan2(x)1-1]/cos2(x)+sin2(x)=sec(x)

Vector Problem 2000-11-27
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?
7 - - - - 77 2000-09-13
From Peter:
Does anyone know how to solve the following:
7 _ _ _ _ 77 ?

I have to find the missing values.

Answered by Chris Fisher and Walter Whiteley.
Some trigonometry 2000-08-11
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).

tan2(theta) = 3 I know sec2(theta) -1 = tan2(theta)

.
.
.

Using the inverse sine function 2000-05-31
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 180-x-y 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*((b2+c2-a2)/(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???

Solve 2sin 3x-1=0 2000-05-11
From Cynthia:
How would you solve 2sin 3x-1=0? I don't know what to do with the 3.
sin(7pi/12) 2000-05-04
From Kristel:
What is the exact value of sin 7pi/12?
Answered by Chris Fisher and Paul Betts.
Triple angle formula 2000-02-23
From Sara:
Can one derive a triple angle formula for sine and cosine? If so, how?
A trig identity 2000-02-17
From Eric:

Question:
How do I solve this problem?

` sin3x   cos3x _____ - _____ = 2 sinx cosx `

Euclidean Math puzzle 2000-01-24
From Margaret Matthews:

(Check out this web-site: Simeon's Triangle Puzzle )

I have tried to figure out how this could be, because everything I know about it tells me it can't be. However, I can't seem to make it NOT work.

Two right angle triangles. They are each cut up into four identical pieces. In the first, all the pieces fit together so that there are NO empty spaces; in the second, presumed to be identical in size to the first, the pieces are slightly rearranged, and now, there IS a space in the triangle.

Answered by Patrick Maidorn and Claude Tardif.
Graph of a sine function 1999-12-23
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.

Passing trains 1999-12-10
From Nancy:
Two trains, each of 80 cars, must pass on a single track which has a deadend siding. How can they pass if the siding can only hold a locomotive and 40 cars?

I do not understand this...help. It will be due monday. I thought it would be simple if the siding could hold 80 cars.

Sines & cosine laws 1999-12-10
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.

Cos x = -1/2 1999-12-01
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.

Crossing number 1999-11-06
From Christian:
The crossing number of a graph G, denoted cr(G) is defined to be the minimum number of (pairwise) crossings of edges among all drawings of the graph in the plane. For example, cr(K5)=1 and cr(K3,3)=1.
What is cr(K7,7)?

I figured out that the answer is 81.

Now I am trying to figure out if K7,7 can be drawn in the plane with less than 81 crossings?

I'm not sure how to approach this one. Other than actually drawing it out and checking by trial and error, I am not sure how to approach this problem. Please help!

Find the missing numbers 1999-10-12
From Bonnie:
I must find the missing numbers and function rules

noutput
710
1220
3940
2430
16b
87c

we are totally confused can someone help

sin x = x/10 1999-10-07
From Amandeep Grover:
Solve the equation sin x = x/10
The Bellhop Problem 1999-08-29
From Gerard O'Neill:
Three fellows going to a Math Conference book into a motel. "That will be \$30.00" says the bellhop. Each fellow gives \$10.00 and they go off to their room. The manager enters and says "That was a \$25.00 room. Go and give them \$5.00 back."
The bellhop heads off but thinks....."how am I going to split \$5.00 between 3 fellows? Hey I will keep two dollars and give each guy a dollar." He does just that.......each fellow now paid \$9.00 and the bellhop kept two. 3 X 9= 27 plus the bellhops two = \$29.00 Where is the missing dollar?

A Trigonometry Question 1999-08-28
From Diane Simms:
My question is can the following be factored. I am a teacher who needs the factors to this right away. 2 Sin2X + 2 SinX CosX - 1= 0
From an airport control tower 1999-08-04
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

Sin 4A 1999-06-22
From Ryan Cochrane:
If sinA = 4/5, and A is a first quadrant angle, find sin4A
Bill and Sam at the Casino 1999-04-23
From Rham Stewart:
Bill and Sam went off to bet at the casino. Each started with the same number of dollars. At the end of the first hour, Bill had won 20\$ and sam had lost 20\$. At the end of the second hour, BIll had lost two thirds of his money, and Sam had won the same amount that Bill had lost. At that point, sam had four times as much money as BIll. How much did each one start with?
Reversing the direction of an inequality. 1999-03-06
From Mallory White:
If the Problem was -4a plus -5 is less than or equal to 14, why would you change the sign to greater than or equal to?
Answered by Jack LeSage and Harley Weston.
Cos(x) Cos(2x) Cos(4x)=1/8 1997-09-24
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 1997-09-18
From Brian Ray:
What is the limit, as x approaches 0, or tan^23x/x^2? (read, tan squared 3x over...)?
Finding the Mine 1997-06-23
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.
...

A problem with arccos. 1997-06-09
From Vanessa Chan:
Prove: arc cos4/5 + arc cos (-5/13) = arc cos (-56/65)
Ajax, Beverley, Canton and Dilltown 1997-03-14
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 1996-12-13
From S. Johnson:
sin t + cos t = 1/5. Find ALL exact values of cot t, given the original equation.
Height of a Hotel 1996-11-07
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?
A trig identity 1996-03-11
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)?
Magic Square 1995-10-20
From Marianne and Carrie:
How can an 8 by 8 square have the same area as a 5 by 13 rectangle?
sup {sin n, n est un entier } 2006-12-17
sup {sin n, n est un entier }
probleme sin cos 2006-02-19
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'est-ce qui fait que l'on trouve ce resultat??