# Homework Help: Math: Trigonometry

## Recent Homework Questions About Trigonometry

trigonometry (Trig Equation)
4 cos 2x + 3 cos x = 1

Trig
If tan theta = a/b, where a and b are positive, and if theta lies in quadrant III, find sin theta

Trig
The Leaning Tower of Pisa is 55m tall. The tope edge of the tower is 5m out from the bottom edge. What is the angle created between the ground and the tower? Round your answer to the nearest degree. tan -1 (55/5) = 85 degrees but my Brother says I did it wrong that the angle ...

Purdue Trig
A spherical balloon is being inflated so that radius is increasing at a rate of 10 mm/sec.

One more problem.. Given sin t= 3/11 and cos t<0, find the values of the remaining 6 trig functions.

Given cos 67.5° = [√(2+√2)]/2, find tan 67.5° , simplify where needed, and show work. I'm starting to learn this stuff, and I'm so confused where to start. I know they gave me the coordinate X as in cos 67.5° = [√(2+√2)]/2, and I also know that tan...

Functions & Trig
evaluate each function at the given value: f(n)=-n^6+31n^4+26n^3+20n^2+-33n-20 when n=6 I was thinking that I should do synthetic division, but I've tried it a few times and I can't get it to work out correctly. Please help!

Functions & Trig
evaluate each function at the given value: f(n)=-n^6+31n^4+26n^3+20n^2+-33n-20 when n=6 I was thinking that I should do synthetic division, but I've tried it a few times and I can't get it to work out correctly. Please help!

trig
Two ships leave port at the same time and travel straight line distances, the first at 30 km/h and the second at 10 km/h. Two hours later they are 50 km apart. What is the angle between their courses?

trig
In a certain right triangle, the two sides that are perpendicular to each other have lengths h = 4.40 m and b = 8.70 m. What is the length of the third side of the triangle?

Calculus
Use the identity sin^2x+cos^2x=1 and the fact that sin^2x and cos^2x are mirror images in [0,pi/2], evaluate the integral from (0-pi/2) of sin^2xdx. I know how to calculate the integral using another trig identity, but I'm confused about how to solve this one.

Trig
Distance between the goal posts, 19.5 feet, is the length of an arc on a circle of radius 50 yards. The kicker aims to kick the ball midway between the uprights. To score a field goal, what is the maximum number of degrees that the actual trajectory can deviate from the ...

Calculus
Use the identity sin^2x+cos^2x=1 and the fact that sin^2x and cos^2x are mirror images in [0,pi/2], evaluate the integral from (0-pi/2) of sin^2xdx. I know how to calculate the integral using another trig identity, but I'm confused about how to solve this one.

Trig
An air traffic controller tells the pilot of an airplane flying due east to turn the plane so that it has a heading of 120 degrees east of north. What angle does the airplane turn and which direction is the plane now headed?

Trig - 9th grade
Can you help me solve: 5sin2x + 3sinx - 1 = 0 Thanks

Calculus
∫((cos^3(x)/(1-sin^(2)) What is the derivative of that integral? I have been trying to use trig identities but can't find one to simplify this equation. I can't find one for (cos^3(x) or (1-sin^(2)) My options -sin(x) + C sin(x) + C (1/4)cos^(4)(x) + C None of these

Trig
Help me find out how to do csc5pi over6

Pre-calculus/ trig
Given the vectors a= (-1,9) and b= (4,2) explain the difference between a-b and b-a. Thank you for your help! :)

Math
Find an equation for the tangent to the curve y=1+ (sqrt2)(csc(X)) + cot(X). I just learned, though my teacher wasn't super good with explaining, derivatives for trig functions but they still aren't making too much sense. Could you please give me a step by step solution for ...

Trig
(tan/cot)- (sec/ cos) Also I need help with tan sin +cos = sec

Trig
(Cos/1-sin)- tan

Trig
Tan^2= csc^2 tan^2 -1

Trig
(Tan/cot)- (sec/cos)

Trig
(Cos/1-sin)- tan

algebra 2 trig
lighthouse b is 9 miles west of lighthouse A. a boat leaves A and sails 5 miles. At this time, it is sighted from B. If the bearing of the boat from B is N64 E, how far from B is the boat?

Trig
In still air, an airplane is flying at 100 mph. It encounters a wind blowing toward the west at 50 mph. What should be the plane's compass heading for its course to be N30ºW?

trig
find the exact value of each expression. do not use a calculator. Sec 3.14/4 + 2 csc 3.14/3 4 + tan 2*3.14/3

Math
Solve simultaneously for the two equations for x and y 5x(cos 45) + 15y(cos 30) = 2,000 5x(sin45) - 15y(sin 30) = 0 I tried adding these two eqn. to elimate y and solve for x by adding [5 x cos 45] and [5 x sin 45] but the value for x is too high. Would I have to use trig ...

Graphing Reciprocal Trig Functions
a) y=csc(x-3) I understand that there are asymptotes at 0, pi, and 2pi and I know how to graph the base points but I am confused on how to move it with the phase shift. Do I use a table of value for the asymptotes and base points to move?

Solving Trig Equations
Solve for x in the interval [-pi,0] a) sin^2x = 3/4 I know that you have +root3/2 and -root3/2 and the positive one gives you an error when doing the inverse of sin, but im confused about the -root3/2. I found that one of the answers of x is -pi/3 (-60 degrees) which fits my ...

Precalc Trig
here's the question: solve for cos(2theta)=1 if you graph r= cos(2Theta) then graph r=1 you find that there are four places where the graphs intersect. however, when solved algebraically, there are two solutions which can be represented in an infinitely many format as: Theta...

Trig right triangle
A ship leaves port at 6 am and heads due east at 20 knots. At 10 am, to avoid a storm the ship changes course to N 47°. Find the ships distance from port at 4 pm.

Trigonometry
Use trig form to find quotient 3/(2+3i)

Trig
A ship leaves port at 6 am and heads due east at 20 knots. At 10 am, to avoid a storm the ship changes course to N 47° E.. (47° east of north). Find the ships distance from port at 4 pm.

Trig
I've done this one multiply times yet it never seems to work out, I'm supposed to simplify yet it never works out tan(csc^-1(x/x-1)) my first step; sin/cos(1/sin(x/x-1))

Math
The current, I, in amperes, for an electric circuit is given by the formula I=4.3sin120(pi)t, where t is time, in seconds. a)At what time is the current at its max volume? How does your understanding of co terminal angles help in your solution? b)What time is the current at ...

Trig
Find all angles θ between 0° and 180° satisfying the given equation. (Enter your answers as a comma-separated list. Round your answers to one decimal place.) Sin θ = 1/4

Calculus
how do you solve this trig identity? i don't get it at all! cos(a+b)cos(a-b)=cos^2a-cos^2b-1

trig
The angle of elevation from a point on the ground to the top of a tree is 38.7 degrees. The angle of elevation from a point 27 ft farther back to the top of the tree is 22.9 degrees. Find the height of the tree to 2 decimal places.

Physics
In a fast-pitch softball game the pitcher is impressive to watch, as she delivers a pitch by rapidly whirling her arm around so that the ball in her hand moves in a circle. In one instance, the radius of the circle is 0.608 m. At one point on this circle, the ball has an ...

trig
Find the component form of v and sketch the specified vector operations geometrically, where u = 4i − j, and w = i + 5j. v = −u + w v = ( , )

trig
Find the magnitude and direction angle of the vector v. v = 4(cos 125°i + sin 125°j) ||v|| = θ =

trig
Find the component form of v given its magnitude and the angle it makes with the positive x-axis. Sketch v. Magnitude Angle ||v||= 7/2 45 degrees v=( , )

trig
An airplane is flying in the direction 148° with an airspeed of u = 920 kilometers per hour. Because of the wind, its groundspeed and direction are v = 820 kilometers per hour and 140°, respectively (see figure). Find the direction and speed of the wind.

Trig application
I can't figure this out. A famous golfer tees off on a long, straight 459 yard par 4 and slices his drive 10 degrees to the right of the line from tee to the hole. If the drive went 288 yards, how many yards will the golfer's second shot have to be to reach the hole?

Trig
I need help with this application. A pier 1250 meters long extends at an angle from the shoreline. A surveyor walks to a point 1500 meters down the shoreline from the pier and measures the angle formed by the ends of the pier. It is found to be 53 degrees. What acute angle ( ...

Math
Find the exact value of the trig expression given that sin u = -5/13 and cos v = -4/5. u and v are in the second quadrant. cos(v - u)

trig
an electric hoist is used to life a piece of equipment y = 2.6 feet. the diameter on the hoist is x = 12 inches. find the number of degrees through which the drum must rotate (round to the nearest integer). *I do apologize, there is a figure in my question, but I cannot paste ...

Trig
mercury rotates around the sun in approx. 89 earth days (or 7,689,600 s. use a calculator to approximate its angular speed. choices: 4.09x10^-7 0.035 0.071 8.17x10^-7

Trig
a smokestack is 190 feet high. a guy wire must be fastened to the stack 30.0 feet from the top. the guy wire makes an angle of 39.0deg with the ground. find the length of the guy wire

Math (Trig)
A ship leaves port at noon and has a bearing of S 25° W. The ship sails at 15 knots. How many nautical miles south and how many nautical miles west does the ship travel by 6:00 P.M.? (Round your answers to two decimal places.) Miles South? Miles West?

Trig
The width of the box is 9 inch more than its length and the height of the box is 1 inch less than its length write an expression for the volume of the box

functions and trig
write the transformation of X cubed if it is shifted right four units and then reflected over the X axis

physics
The problem propmpts us with the info: "Two friends play with a card-board box on a grassy hill side. The boy in the box has a mass of 50.0 kg and the box has a mass of 5.00 kg. The incline of the hill is 44° and its height is 10 meter. Assume that friction plays a negligible...

trig
given cotθ = (1/2) √7, find sinθ and cosθ in quadrant I cotθ = x/y would 1/2 be the x and √7 be the y?

trig
1) given cotθ = 1/2√7, find sinθ and cosθ in quadrant I 2) given tanθ = √5, find secθ and cotθ in quadrant III

precalculus
find the values of the requested trig functions using the given value and quadrant in which the point corresponding to the angle lies. quadrant II; sinθ=4/5 find cosθ and tan θ

math
identify all of the basic trig functions that fit each description. 1) is negative for angles in the 2nd and 4th quadrant 2) is unbounded answer: tan, cot 3) has a range of -1 ≤ y ≤ 1 answer: sin, cos are my answers correct? and i'm not sure what the answer to ...

Trig
Having completed another stimulating school day, Michael and Alyssia both leave at the same time. They walk together for a while and then go their separate ways. These paths make a 60° angle with one another. Michael toddles along at 2ft/sec, while Alyssia speeds off at 3ft/...

Physics/trig
A fire hose ejects a stream of water at an angle of 33.6 ° above the horizontal. The water leaves the nozzle with a speed of 29.6 m/s. Assuming that the water behaves like a projectile, how far from a building should the fire hose be located to hit the highest possible fire?

trig
1) cos^2(x)/sin^2(x) 2) tan(x)cot(x)-sin^2(x) 3) 1-sin(x)cos(x)tan(x)

Math (Trig)
A triangle ABC has a trisected angle A. The angle trisectors divide side a (opposite angle A) into three segments which are BD, DE, and DC. The lengths are 2, 3, and 6, respectively. What are the lengths of the other sides?

trig
The angle relative to the horizontal from the top of a tree to a point 12 feet from its base(on flat ground) is 30*. Find the height of the tree.

calculus
1. what trig function has an amplitue of 1 and negative values for angles between π/2 and π? 2. what trig function never crosses the x-axis and has a value of 2 at π/6? are these correct? 3. what trig function has a period of π and is undefined for -π/...

trig
A skateboard wheel has a radius of 2.08 inches and is turning at a rate of 945 rpm. a. what is the angular speed in radians per second? in degrees per second? b. how fast is the skateboard traveling (in miles per hour)?

Precalc
Identify all of the trig functions that fit each description: 1. Has a amplitude of 1 2. Is discontinuous at odd multiples of π/2 3. Is continuous at odd multiples of π/2 4. Has sin x as a denominator value 5. Is completely bounded 6. Has the exxact same value at &#...

Trigonometry
find the value for the indicated trig function for ø, if ø is an angle in standard position with the terminal side defined by the given point. (18,24); find cos ø

Trig
The foot of a ladder is on level ground 1.5m from a wall. The ladder leans agents the wall. The angle formed by the ladder and the ground is 70 degrees. Calculate how high up the wall the ladder reaches.

trig
If each leg has length 5 meters, what are the lengths of the other leg and the hypotenuse

Math Trig
A plane's flight path called for it to fly from J to W. W is 200kms due North and 500kms due west of J. Draw a coordinate picture. What bearing will the pilot fly and what distance will he or she go in air kilometers?

Physics/trig
During takeoff, an airplane climbs with a speed of 300 m/s at an angle of 36 degrees above the horizontal. The speed and direction of the airplane constitute a vector quantity known as the velocity. The sun is shining directly overhead. How fast is the shadow of the plane ...

Trig
Evaluate the following expression: sin(cos^-1(12/13)) tan(sin^-1(3/5)) I do not know what the inverse values would be...how would I work through this?

Trig
Find all solutions of the equation in the interval [0,2pi). 2sin theta+1=0. Write answer in radians in terms of pi.

Trig
cos 13 pi = ?

math trig
Solve for x if 3sin2x - 3sinx = 2 - 4cosx 0<x<180

trig
If sinx=3 cosx, then what is sinx∙cosx?

Trig
Solve, algebraically or with justification (no graphing calculator solutions allowed), the following equation: tan⁡7x-sin⁡6x=cos⁡4x-c​ot⁡7x

Trig
What is the value of tan⁡x given that sin⁡x+cos⁡x=1/5 and π/2<x<π ?

Trig
Algebraically find the value of: 10 cot⁡(cot^(-1)⁡3+cot^(-1)R​89;7+cot^(-1)⁡13+cot^(-1)⁡21​ )

Trig
Write an algebraic expression for the following: sin⁡(arctan⁡〖(x+1)/(x​-1)〗 )

Trig
Prove the identity: (sin⁡(2x-y)+sin⁡y)/(cos̼​9;(2x-y)+cos⁡y )=tan⁡x

trig
The hypotenuse of a right triangle has length 8. The area of the triangle is also 8 units squared. What is the perimeter of the triangle?

trig
what is terminal point of 5pi/4?

trig
A road has a 10% grade (slope). To the nearest degree what is the angle of elevation of the road?

Maths trig
Sketch the graphs of f(x)=3overx+1 and g(x)=-2x-4 on the same set of axes

Maths trig
Sketch the graphs of f(x)=3overx+1 and g(x)=-2x-4

trig
Help with simplest form sin(2pift - pi) + sin(2pift + pi)

trig
A radio transmission tower is 471.0 feet tall. A guy wire is to be attached 6 feet from the top and is to make an angle of 23.1 degrees with the ground? How many feet long should the guy wire be? I am confused on how to find the equation for this problem so that I may work it ...

Trig/ algebra 2
if f(x) = sin4x-cos2x, find f(pi/8)

Trig/Geometry
Wendy spots a pizza delivery car as she is looking down at a 15° angle from the top of her apartment building, which is 145 ft tall. How far away is the car from the base of the building? Round to the nearest hundredth. A. 45.98 ft B. 3.56 ft C. 38.85 ft D. 68.78 ft I keep ...

trig
An airplane is heading north at an airspeed of 500 km/hr, but there is a wind blowing from the northwest at 50 km/hr. how many degrees off course will the plane end up flying, and what is the plane's speed relative to the ground? So here is my work... 50cos(45)+500= 535.355 ...

Trig
Find sin2theta, cos2theta, and tan2theta for costheta = -12/13 in pi < theta < 3pi/2. My answers: 20111/24336 for tan2theta. 144/169 for cos2theta -120/338 for sin2theta

Trig
For 90<theta<180, cos theta = -(5/13). Which is sin theta? 1. - sqrt 13/9 2. - sqrt 9/13 3. sqrt 9/13 4. sqrt 13/9 3?

Trig
Which is cos2 theta if sin theta = -2/sqrt13 and 180 < theta < 270? 1. -(13/5) 2. -(5/13) 3. 5/13 4. 13/5 3?

algebra 2 and trig
The scores on a chemistry test are normally distributed. Approximately 95 percent of the scores fell between 78 and 92. What is the standard deviation for this distribution?

Trig
Solve each equation for the given domain. cos^2 theta + cos theta - 1 = 0 for 0-180.

Trig
Solve the equation for the given domain. 4cos^2 θ = 1 for 0 to 360 degrees. I get 60, 120, 240, and 300. Are these correct? If so, how would I represent them with some sort of expression?

Trig Identities
Prove the following identities: 13. tan(x) + sec(x) = (cos(x)) / (1-sin(x)) *Sorry for any confusing parenthesis.* My work: I simplified the left side to a. ((sinx) / (cosx)) + (1 / cosx) , then b. (sinx + 1) / cosx = (cos(x)) / (1-sin(x)) I don't know how to verify the rest.

Trig identities
Sin x/[1-cos(-x)] = csc x + cot x Please Verify the Identity. I have been going in circle with this one... Just a hint would be nice. Thank you.

trig
a vertical pole 35 feet high, standing on sloping ground, is braced by a wire which extends from the top of the pole to a point on the ground 25 feet from the foot of the pole. If the pole subtends an angle of 30 degree at the point where the wire reaches the ground, how long ...

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