# Homework Help: Math: Trigonometry

## Recent Homework Questions About Trigonometry

trig
what is the exact value of tan 105 degrees

trig
If a ship leaves port at 9:00 a.m. and sails due south for 3 hours at 14 knots, then turns N 60° E for another 2 hours, how far from port is the ship?

trig
If a ship leaves port at 9:00 a.m. and sails due north for 3 hours at 12 knots, then turns N 30° E for another hour, how far from port is the ship?

Math (Trig)
Suppose the point A is on a circle of radius 6 with an angle of 240 degrees. Find the value of the coordinates of this point. Round your results to 3 decimal places. So in this case, x=rcos(theta) y=rsin(theta) x=6cos(240) y=6sin(240) Rounding to 3 decimal places: x=-3 y=-5....

Math (Right Triangle Trig)
Suppose tan(theta)=5/7 and theta belongs to Quadrant III, find the exact value of sec(theta)? I already took the steps to solve this problem but I am confused if whether or not sec(theta)is positive or negative sqrt(74)/7 Any help is greatly appreciated!

Trig
6. To win a javelin throwing competition, your last throw must travel a horizontal distance of at least 100 feet. You release the javelin at a 40° angle with an initial speed of 71 feet per second. Do you win the competition? Justify your answer

Math trig
Hello guys. I am just wondering if tan^2 A (tan squared A) = sin^2 A /cos^2A And 2tan A = 2sin A / 2cos A This has been bothering me when I have to simplify trig. Thanks in advance.

Trig
If sin(theta) = 3/7, what is sin (pi/2 - theta)?

Math (Trig)
Convert the Cartesian coordinate (-1,2) to polar coordinates, 0≤θ<2π I know r is sqrt(5) but how would I find theta between 0 and 2pi? Thanks in advance!

Math (Trig)
A clock tower has been constructed such that the center of the clock is 40 feet above ground. The minute hand on the clock is 3 feet long. How far above the ground the end of the minute hand at 12:05? 1:00?

geometry and trig
If a cylinder with a 4 inch diameter and a 6 inch height holds 1 pound of oatmeal. How much oatmeal will a cylinder (similar) with a 10 inch diameter hold? Volume of 4 in-----24pi volume of 10 in----137pi I get 91 oz choiced are37,44,74, 192

Math (Trig) lowering powers
If cos^4(3x)-sin^4(3x)=cos(g(x)) then g(x)=? Use a^4-b^4=(a^2-b^2)(a^2+b^2)! thanks in advance for any help!

trig
sec = 7/2 and is in Q1, then what is double angle of tan?

Trig
Two rays with common endpoint O form a 30 degree angle. Point A lies on one ray, point B on the other ray, and AB=1. What is the maximum possible length of OB?

Pre-Cal (Trig) Help?
The following relationship is known to be true for two angles A and B: cos(A)cos(B)-sin(A)sin(B)=0.957269 Express A in terms of the angle B. Work in degrees and report numeric values accurate to 2 decimal places. So I'm pretty lost on how to even begin this problem. I do know ...

trig, precalc, math, algebra, trigonometry

trig
sin 25° cos 35° + cos 25° sin 35°

Trig
find the equation for the cosine function that has an amplitude of 3/5, a period of 3pi/2 and a y-intercept of 5.

Math -Trig
Determine the exact value if cot(3pi/4) using special triangles. I don't understand how it could be 1/tan3pi/4 in a triangle....

Math - Trig
if the diameter of a tire is 3.5 m and makes one rotation every 5 seconds, how far does the tire rotates in one minute?

Geometry/Trig
In triangle ABC, A is a right angle, and m b=45 degrees. What is the length of BC? If your answer is not an integer, leave it in simplest radical form. a. 16 ft b. 16 sq 2 ft c. 16 sq 3 ft d. 32 ft I'm really confused as to how to do this... Could someone please explain and ...

trig
tan(theta)/tan(2theta)-tan(theta)= cos(2theta)

Trig
Problem: A cable from the top of a 60 foot high tower is to be attached to the ground (x) feet from the base of the tower. A) if the cable makes an angle of t radians with the ground when attached, express t as a function of x. B) if t = pi/5, how far is the end of the cable ...

Trig
Solve each equation for exact solutions over the interval [0,360)where appropriate. Round approximate solutions to the nearest tenth degree. Sin^2Theta=Cos^2Theta+1 My Work: Using double angle Identity I subtract 1 to other side therefore: 1-Sin^2theta=Cos^2theta= Cos2theta=...

Trig
While fishing on a lake, the fisherman looks up at a cliff. His boat is 23 ft from the base of the cliff, and the angle of elevation is 40 degrees. Find the height of the cliff to the nearest tenth of a foot.

trig
A car is traveling at 34 miles per hour. If its tires have a diameter of 14 inches, how fast are the car’s tires turning? Express the answer in revolutions per minute and round to two decimal places.

trig
A car is traveling at 34 miles per hour. If its tires have a diameter of 14 inches, how fast are the car’s tires turning? Express the answer in revolutions per minute and round to two decimal places.

Trig
Days 0 2 4 6 8 10 12 14 16 Lions (number) 1272 1523 1152 891 1284 1543 1128 917 1185 Deer (number) 39 47 63 54 37 48 60 46 40 Find a sin Equation for Lions and deer. use this model. Thanks! y=k + A sin (Bx+C)

trig
Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place.) a = 63, c = 50, ∠C = 53°

Math-Trig
Answer to four significant figures, or to the nearest minute. f) one vertex angle of a rhombus is 25°. Find the ratio of the diagonals.

Trig
A small plane takes off from island A and flies in a straight line for 12 kilometers. At the same time, a sailor sitting in a sailboat who is 5 miles from the island measures the angled by from island A to the sailboat and the plane is 37 degrees. How far is the plane from ...

Trig
A Flagpole casts a 60 foot long shadow on the ground. The angle from the tip of the flagpole to the end of the flagpole's shadow measures 35 degrees. How tall is the flagpole? can i use tan(35degrees) = 60/h which gives me 85.714. Please check. Thanks!

A Flagpole casts a 60 foot long shadow on the ground. The angle from the tip of the flagpole to the end of the flagpole's shadow measures 35 degrees. How tall is the flagpole? can i use cos(55degrees) = 60/h which gives me 104.61. Please check. Thanks!

Trig
A Flagpole casts a 60 foot long shadow on the ground. The angle from the tip of the flagpole to the end of the flagpole's shadow measures 35 degrees. How tall is the flagpole? Draw a picture and label. Thank you.

Math Trig
use a double-angle formula to find the exact value of cos2u when sinu=5/13 , where pi/2<u<pi So far I went cos2u=1-sin^2 =1-2(25/169) =1-(50/169)

Trig
If the terminal side of an angle theta contains the point (-1,3), find secant theta.

Trig
Find sin(x+y), cos(x-y), tan(x+y), and the quadrant of (x+y) if sinx= -1/4, cosy= -4/5, with x and y in quadrant 3.

trig
The minute hand of a clock is 7 inches long and moves from 12 to 11 ​o'clock. How far does the tip of the minute hand​ move? Express your answer in terms of pi and then round to two decimal places.

Trig
Find the length of a chord intercepted by a central angle of 25 degrees in a circle of radius 30 feet

trig
2(sinx)^2-5cosx-4=0 Solve for all solutions between [0,2pi]

Trig
suppose that the angle theta is in the second quadrant, and that sin(theta)=1/3. Find exact values for cos (theta) and csc (theta)

Solve cos315*cos(-390)-sin225*sin750 cos315: <RA = 360-315 = 45 cos45 = 1/√2 cos-390: <RA=-390+360 =30 cos30= √3/2 sin225: <RA = 225-180 = 45 Sin45=1/√2 Sin750: <RA = 750 - 2(360) =30 Sin30=1/2 Put it all together... (1/√2)(√3/2)-(1/&#...

Trig
How do I write cos(11x)cos(x)+sin(11x)sin(x) as a single trigonometric function? Please show steps.

trig
Angle θ lies in the second quadrant, and sin θ = 3/5. Find cos θ and tan θ.

Trig
Find the exact values of sec(x)=7. I know that cos(x)=1/7. I know that sin(x)= sqrt(1-91/4900). I know that tan(x)=1. I know how to do the problem but I'm not really sure why, and I'd like to know. I got 4sqrt(3). Please help!

trig
Which expression is equivalent to tan(-x)cos^2x? -sin xcos x sin xcos x tan x + sin2x tan x − sin2x -tan x − sin2x

Trig
If tan A= 3/4 and cos B=-5/13, where A and B are both third-quadrant angles, find sin(A+B). Please explain how you found all the answers

geometry and trig
I have a regular octagon with a radius of 9. I have split the 8 pie slices into right angles--leaving angles 90, 67.5, and 22.5. I looked for the sine of 22.5 opp/hyp and get .38. Then the oppositeside is 6.84. I can't get the right answer, what am I doing wrong? Thanks

Trig Help
Given the equation for simple harmonic method d=1.3cos(3pi/4 t) answer the following questions: a)Find the maximum displacement. 1.i got 1.3 b)Find the frequency and length of the pendulum c)Calculate the value of d when t=3 i got .919 d)Determine the least positive value of t...

Trig
Find the algebraic expression that is equal to sec theta - cos (-theta)

Trig
find the algebraic expression that is equal to sin (-theta) sec(-theta) cot(-theta)

trig
Simplify and write the trigonometric expression in terms of sine and cosine: cot(-x)cos(-x)+sin(-x)=-1/f(x)=f(x)=____​________ I've tried everything, I think that the "-1/f(x)" part is screwing up my answer but I'm not sure what it's asking me to do with that?

trig
a building 60 feet high. from a distance at point A on the ground, the angle of elevation to the top of the building is 40 degree. from a little nearer at point B, the angle of elevation to the top of the building is 70 degree. What's the distance between point A and B ?

Trig identity.
I need help with verifying these trig identities: 1) sin4x = 4sinxcos - 8sin^3 x cos x 2) cos3x = cos^3 x - 3sin^2 x cos x

Trig help
Can someone help me find ALL solutions in the interval [0,2π) for the given equations. Please show work. 1) sin2x = sin2x 2) tan2x +tanx = 0

Trig
I have a diagram of how far a discus was thrown. From A to B is 100m, C is perpendicular to A, from A to C is 50m, A and B are connected to D (it should be a triangle), A has a 40° angle and B has a 75° angle. C is not perpendicular to D btw.. a. Find AD and use it to find ...

Trig
The original screamer radius =100 feet rotated 1 deg per sec. The engg decided to make it scarier by making it rotate 18 deg per second. Write the new equation for the vertical position of a passenger on the screamer where the domain is now the time per revolution (in sec)

Trig - Ambiguous Cases
Triangle HAV has <H = 124, a=8.5mm, and h=7.2mm How many solutions are there? What I attempted: SinH/h=SinA/a Sin124/7.2=SinA/8.5 SinA=8.5(Sin124/7.2) <A = 78.2 RULE => All interior angles must add up to 180 degrees therefore this triangle has 0 solutions. The ...

trig
half angle formula to find exact value cos 112.5 degree

trig
sin^4x

trig
sin 2x-cot x=

trig
Find all solutions in the interval [0,2π) for cos(x - π/6) = 1 + cos(x + π/6). Show work, please and state in solution set.

The height h in inches of pistons 1 and 2 in an automobile engine can be modeled by h1 = 3.75sin(733t) + 7.5 and h2 = 3.75sin[733(t+ 4π/3)] + 7.5 where t is measured in seconds. How often are these two pistons at the same height? Show work please.

Trig
Given sin= -√5/6 with π < u < 3π/2 and cos v= √3/5 with 0 < v < π/2 find sin(u-v) and tan(u+v). Please show work and simplify.

Write the augmented matrix, and then solve the system, using Gauss Jordan elimination on the augmented matrix. x + 2y - z = 4 -2x + y - 4z = -6 4x - 3y + 2z = -10

trig
Solve for sin4x=sin2x?

trig plz help
Solve. Round off your answer to the nearest foot. (The picture is not drawn to scale.) A balloon is 1500 feet above the ground. The angle of depression from the balloon to headquarters is 46°21'. How far is the headquarters from a point on the ground directly below the ...

trig
Find the exact values requested. No decimal approximations. Given that cot θ = 4 for an acute angle θ, A. Find sinθ. B. Find cos(2θ).

trig
verify (csc^4-1)/cot^2x=2+cot^2x So this is what I have so far on the left side (csc^2x+1)(cscx+1)(cscx-1)/cot^2x =(csc^2x+1)(cot^2x)/cot^2x i think I'm doing something wrong. Please help!

trig plz help
Solve, finding all solutions in the interval [0, 2π). tan(3x) = -1

trig gauss jordan
Write the augmented matrix, and then solve the system, using Gauss Jordan elimination on the augmented matrix. x + 2y - z = 4 -2x + y - 4z = -6 4x - 3y + 2z = -10

trig help
Find the equation of the hyperbola satisfying the given conditions. Vertices at (5, 1) and (-7, 1); asymptotes (y - 1) = 1/3(x + 1) and (y - 1) = -1/3(x + 1)

last 2 questions trig!!
4. Solve the triangle(s), if possible. Round to the nearest tenth. Solve the triangle. Side a = 8, side b = 10, side c = 12 6. Two boats leave the same dock at the same time. The first sails in a straight line N40°W at 36 miles per hour and the second goes in a straight line ...

math 108 trig
1.Solve, finding all solutions in [0, 2π). cosx sin2x + sinx cosx - sinx = 0 2.Solve, finding all solutions in [0, 2π). 3sec x = 2tan^2x

plz help trig!!!!!
A boat sails 20 km in a direction of N75°E. Draw the 20 km travelled in a direction of N75°E as a vector v in standard position. Find the component form of the vector v. Round your answers to the nearest hundredth. 2 pts. B. Next, the boat turns and sails 10 km in a ...

trig plz help
A boat sails 20 km in a direction of N75°E. Draw the 20 km travelled in a direction of N75°E as a vector v in standard position. Find the component form of the vector v. Round your answers to the nearest hundredth.

trig exact vales
Find the exact values requested. No decimal approximations. Given that cot θ = 4 for an acute angle θ, A. Find sinθ. B. Find cos(2θ).

trig/ellipse equation
Find an equation of an ellipse satisfying the given conditions: Vertices: (-1, -8) and (-1, 4); and the length of the minor axis is 10.

Calculus
Integrate dx/(sqrt(x^2+16)). I have no idea how to start and which method to use. Thinking some sort of trig substitution? But it doesn't look like it. Step by step? Answer key says ln|x+ sqrt(x^2+16)|.

Trig
Solve for [0,2pi) 2cos4x + sqrt3 = 0

trig
A wheel with a 22 inch diameter is turning at the rate of 31 revolutions per minute. What is the linear speed of a point on the rim, measured to the nearest inch per minute?

trig
From a boat on the bay, the angle of elevation to the top of a cliff is 29°10’. If the bottom of the cliff is 1860 feet from the boat, how high is the cliff (to the nearest foot)? Assume that a right triangle is formed.

Trig application
A man is holding a gun 4 feet above the ground and fires into an open field. The bullet has an initial velocity of 300 feet per second and an initial angle of 30°. Find the range (the horizontal distance traveled before hitting the ground ) and the bullet's max height. Please...

Trig application
I'm having trouble with this trig application. The scenario goes: A ferris wheel has a diameter of approximately 65 meters. Assume it takes 110 seconds for the ferris wheel to make one complete rotation. find the angular speed of the ferris wheel in radians per minute and ...

Trig
Use the Law of Cosines to determine the indicated angle θ. (Assume a = 17, b = 10, and c = 20. Round your answer to one decimal place.)

trig
A ship is passing through the island of corregidor. at its closest point of approach, Corregidor radar determines that it is 2, 400 meters away. Later, the radar determines that it is 2, 650 meters away. a.) By what angle did the ship's bearing from corregidor change? b.) How ...

Trig
Find the arc length of a circle that has a central angle of 270 degrees and a radius of 10 yards.

Trig
The Stratosphere Tower is Las Vega dominate the city's landscape by rising 1,149 feet above the desert floor. The restaurant at the top of the tower turns slowly and completes a full revolution in one hour. How many radians will the restaurant have rotated in 52 minutes?

Trig Identities
Why does cos^2(x)= 1/2cos(2x)+1/2? I am trying to integrate, but the answer key says to first rewrite the expression like the above. I don't get how to change cos^2(x) into that. Explain?

Trig
a road is inclined at an angle of 45degrees. After driving 300 feet along this road, find the driver's increase in altitude.

Trig
a 12-ft-long guy wire is attached to a telephone pole 10.5 ft from the too of the pole. If the water forms a 52 degree angle with the ground, how high is the telephone pole?

Trig application
Can anyone help me with this problem? I'm so confused. Please help. A security camera is placed 27 feet from the counter at a store. The counter is 18 feet long and the camera is placed 4 feet from one end. What angle, to the nearest degree, should the camera rotate through so...

Trig identity inverses
Find the exact value of cos[cot^-1 (-√3) + sin^-1 (-1/2)]. I'm having trouble with inverses. Please help by showing work.

Trig
Find the exact value of csc 4pi/3 What I have determined thus far: 4pi/3 = 60 degrees sin = square root of 3/2

Trig.
If TanTheta= -65/72 and the terminal side of theta lies in Quadrant II use a pythagorean identity to find sec theta.

Trig
Find all values of theta where 0degrees<theta<360 degrees when csc theta = square root 2 Please detail how/why i can get to the solution. I need to understand the concept clearly...... It will probably relate to something taught down the line I'm sure.

Trig
Find all values of theta where 0degrees<theta<360 degrees when csc theta = square root 2

Trig
Find all values of theta where 0degrees<theta<360 degrees when csc theta = square root 2

Trig
If cot theta = -12/5 and the terminal side of theta lies in quadrant II find secant theta

trigonometry (Trig Equation)
sin 3x=-1

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