# Trigonometry

Calculus
S=integral sign S3x(4-x^2)^1/2 use trig substitution I am confused I got x sin(sin^-1(x/2))+cos(sin^-1(x/2))

trig
Suppose that θ is an angle in standard position whose terminal side intersects the unit circle at , −15/17,−8/17

Trig
Jimmy wants to rewrite the set of parametric equations x = 1/2 T + 3 and y = 2T - 1 in rectangular form by eliminating T. Which of the following equations would help him to eliminate T. A) t = 2(x-3) B) t = 2(x+3) C) t = y-1 / 2 D) t = 2(y+1)

Math Trig
I can't seem to get the right answer on my assignment. I keep on getting 276.403 and seem to get it wrong. Please help. Suppose that cot(θ)=−8.91 and 0∘≤θ<360∘ Find the two distinct angles.

Math (Double checking trig identity)
Since sec^2θ - 1 = tan^2θ I know this is trivial, but I want to make sure I'm doing this right before I apply it to the integral I'm trying to solve... If I have some constant a, (a^2secθ)^2 - (a^2)^2 If I wanted to change this to tan would it be: a^4tan^4θ? Any help is ...

Trig
Find the derivative. {sqrt(x+8)}*(x^2+20x) (x+8)^1/2(2x+20) minus (1/2)(x+8)^-1/2(x^2+20x) I'm not feeling confident I am on the right track and I have a quiz tomorrow over this.

Trig
Find the derivative using the product rule. {sqrt(x+8)}*(x^2+20x) (x+8)^1/2(2x+20) minus (1/2)(x+8)^-1/2(x^2+20x) I'm not feeling confident I am on the right track and I have a quiz tomorrow over this.

Trig help
Which of these is equivalent to 3π/5 rad ? A) 108° B) 150° C) 216° D) 300° I'm thinking A

Trig help
Find the cos(Θ) of an angle in standard position if the terminal side passes through the point (4, -8). -2 -2/sqrt5 1/sqrt5 2 I think it is C but I am not so sure.

Math (integrals) (Trig Subsititution)
Find ∫1/((x^2+5)^(3/2)) dx I figured this would be a trig substitution problem, so I set x = sqrt(5)tanθ and dx = sqrt(5)sec^2(θ) dθ This would lead to: ∫(sqrt(5)sec^2(θ)) / (5tan^2(θ) + 5)^(3/2) dθ But I'm kinda lost on what to do next. I'm used to breaking up the ...

trig
To help a sapling (young tree) grow straight, a gardener attaches three guy wires to it and the ground. She places the wires two feet below the top of the tree. If the wires are ten feet long and each makes an angle of 58 degrees with the ground, find the height of the tree to...

trig ratios'
To help a young tree grow straight, a gardener attaches three guy wires to it and the ground. She places the wires two feet below the top of the tree. If the wires are ten feet long and each makes an angle of 58 degrees with the ground. Find the height of the tree.

Algebra/Trig
To ensure safety, the recommended angle that a ladder leaning against a building makes with the ground is 75 degrees. Will a 12 foot ladder reach a window 10 feet above the ground if it leans against the building with this angle? Use trigonometry to justify your answer.

Trig
To help a young tree grow straight, a gardener attaches three guy wires to it and the ground. She places the wires two feet below the top of the tree. If the wires are ten feet long and each makes an angle of 58 degrees with the ground. Find the height of the tree.

Trig
Right triangle PQR with the right angle at Q has one side measuring 46 feet and the hypotenuse measuring 54 feet. Find the other side as a radical in simplified radical form and to the nearest tenth.

Trig
Is a triangle that has sides which measure 8, 15, and 17 a right triangle? Justify your answer, ie,

A smokestack is 200 ft high. A guy wire must be fastened to the stack 30.0 ft from the top. The guy wire makes an angle of 42.0° with the ground. Find the length of the guy wire.

Trig
A conveyor is used to lift paper to a shredder. The most efficient operating angle of elevation for the conveyor is 35.2°. The paper is to be elevated 16.0 m. What length of conveyor is needed?

Trig
The length of a rectangle is 142.9 in. If the diagonal makes an angle of 32.1o with this side, find the measure of the diagonal of the rectangle rounded to the nearest tenth of an inch. let x represent the diagonal.

trig
An airplane has an airspeed of 450 kilometers per hour bearing Upper N45E. The wind velocity is 60 kilometers per hour in the direction Upper N30W. Find the resultant vector representing the path of the plane relative to the ground. What is the ground speed of the​ plane? ...

TRIG
The length of a rectangle is 142.9 in. If the diagonal makes an angle of 32.1o with this side, find the measure of the diagonal of the rectangle rounded to the nearest tenth of an inch. let x represent the diagonal.

Calculus (trig derivatives)
A lighthouse 2 miles offshore has a light that rotates once every 20 seconds. At what rate is the light traveling along the shore if it is shining on a point 4 miles along the shore from the point nearest the lighthouse?

trig
Find all solutions in the interval [0, 360) 8cos^2x+6cosx+1=0

Trig/Pre-Calc
A bird is flying 30 mph in a direction 30 degrees south of east. Affecting the flight of the bird is a wind blowing from the northeast to the southwest at a speed of 10 mph. What is the resulting speed of the bird?

Intro to Trig
Which of the following best corresponds to the x-value where the function f(x)=cos x is a minimum in the interval x = [25,30]? A) 25.1 B)26.7 C)28.3 D)29.8 Can someone show me how to solve this step by step? Thanks :)

Trig
Morana is trolling for salmon in Lak Ontario. She sets the fishing rod so its tip is 1 m above the water and the line enters the water at an angle of 45 degrees. Fish have been tracked at a depth of 45km. What length of line must she let out?

Trig

Trig

Trig

Trig
In which quadrant would the image of point (5,-3) fall after a dilation using a factor of -3?

Trig
Find all solutions of the equation in the interval [0,2pi) 2 cos^2 x-cos x = 0 -2cos^2 + cosx + 0 (x+1/2) (x+0/2) (2x+1) (x+0) -1/2,0 2Pi/3, 4pi/3, pi/2, 3pi/2 my teacher circled pi/2 and 3pi/2 What did I do wrong? I don't understand...

Pre-Calc Trig
Create both a sine and cosine model for height of a passenger off of the ground for each of the following Ferris wheels. 1) customers must climb up 12 foot steps to get into the Ferris wheel (I.e) bottom of Ferris wheel is at the top of the steps Diameter 67ft Rotional speed 1...

Precalculus
Rewrite as single trig function: sin(8x)cosx-cos(8x)sinx I know I can simplify sin(8x) into 4sin2xcos2xcos4x, but I'm stuck after that

Trig
Right circular cylinder A has a volume of 2700 cubic inches and radius of 15 inches. Right circular cylinder B is similar to cylinder A and has a volume of 800 cubic inches. Find the radius of cylinder B.

Trig Identities
secx - sinxtanx

Trig
Find the area of a triangle whose vertices are A(0,2), B (2,7), C (0,10).

Trig
Find the area of quadrilateral whose verties are A(0,2), B(2,7), C(6,10), and D (9,-2).

Trig
what are the intercepts of the graph of f(x)=4cos^2 -3 on the interval [0, 2pi]?

Math
Find the exact value of the trig function below. cos2Ø if sinØ = 2/5

Math
Find the exact value of the trig function below. cos a/2 if cosa = - 31/49 (assume cos a/2 is negative)

Trigonometry
5. If a trig equation has one answer, how many answers will it have? (Provided you do not restrict the domain?) 6. Why are the graphs of the inverse functions restricted to one period of the function? I only need to answer these two to finish my homework and I can't figure out...

Maths Trig
A 60m long bridge has an opening in the middle and both sides open up to let boats pass underneath. The two parts of the bridge floor rise up to a height of 18 m. Through what angle do they move?

Trig
Convert the polar equation to rectangular form. r=4cos-4sin What I have so far: r^2=4rcos-4rsin x^2+y^2-4x+4y x^2-4x+y^2+4y=0

Trig
The vector y has magnitude 5 and direction angle 17°. The vector z has magnitude 3 and direction angle 180°.

Trig
(Tan^2 x) - 2 tan x - 3 / tan x + 1

Math - Trig
Two buildings of equal height are 850 feet apart. An observer on the street between the buildings measures the angles of elevation to the tops of the buildings as 29° and 40°. How​ high, to the nearest​ foot, are the​ buildings? I don't know how to set this up

Trig
When the angle of elevation of the sun is 61°​, a telephone pole that is tilted at an angle of 8° directly away from the sun casts a shadow 20 feet long. Determine the length of the pole to the nearest foot. I'm stuck halfway through this problem, I know how to find all ...

Math Trig
A ladder 15 m long can so be placed that it will reach a point on a wall 10 m above the ground. By tipping it back without moving its feet, it can be made to reach a point on another wall 8 m above the ground. What is the horizontal distance between the walls?

Urgent--Geometry(trig part)
So I am new to sine, cosine, and tangent, so I need some help. Just explain it. No need for the answers unless you want to give it to me. :D Let triangle ABC be a right triangle with angleC=90degrees. Given the tangent of one of the complementary angles of the triangle, find ...

Trig
Find all solutions in the interval [0,2pi) 4sin(x)cos(x)=1 2(2sinxcosx)=1 2sin2x=1 2x=1/2 x= pi/6, and 5pi/6 Then since its 2x i divided these answers by 2 and got pi/12 and 5pi/12 However, when i checked the answer key there solutions 13pi/12 and 17pi/12 were included ...

Trig identies, Calculus
Use the identities cos^2 x + sin^2 x =1 and cos2x=cos^2 x -sin^2 x to show that cos^4 x -sin^4 x = cos2x Im not sure how, I can solve my problem with half angle identities but im not sure where to start with this.

Math - Calc/Algebra/Trig
I'm trying to find all the points on the graph y=4/3cos^3x-cosx where the tangent line is horizontal. I took the derivative, which gave me: -4cos^2(x)sin(x)+sin(x) Now I need to solve it for x and I'm not sure how. Can you help?

Calculus Question! ASAP!
Hello! I have this problem: x(dx)/sqrt(9-x^2) I was wondering why I can't use trig substitution and substitute sqrt(9-x^2) for sqrt(1-sec^2) and having: integral x = 3sin(theta) dx = 3cos(theta)d(theata) integral 3sin(theta)(3cos(theta))/3cos(theta) having the 3cos(theta) ...

Trig
Solve for t algebraically: inverse cos(t) = inverse sin(t). Where do I start?

Alg/Trig
If h= -16t^2 + 112t represents the height of a​ rocket, in​ feet, t seconds after it was​ fired, when will the rocket hit the​ ground? (Hint: The rocket is on the ground when h equals=​0).

Trig Practice
Find the exact value of sinA where a=9 and b=10 and angle C is a right angle. a. sin A= 9/sqrt 181, cos A= sqrt 181/10 b. sin A= sqrt 181/9, cos A= 10/sqrt 181 c. sin A= 9/sqrt 181, cos A= 10/sqrt 181 d. sin A=sqrt181/10, cos A= 9/sqrt 181

trig
in triangle QRS, q=10.2m, r=20.5m, s12.8m..Solvetriangle QRS by determining the measurements of each degree to the nearest tenth of a degree

Trig
4x+y=​0, x≥0 help finding Sin, Cos, Tan for this

Trig
can sec θ = negative 5

trig
sin, cos, and tan for −5x + y =​0, x is less than or equal to 0

Trig
Find the approximate value of cot θ​, given that csc θequals=3.5891420 and θ is in quadrant I.

Geometry/Trig
A painter is placing a ladder to reach the third story window, which is 18 feet above the ground and makes an angle with the ground of 80°. How far out from the building does the base of the ladder need to be positioned? Round your answer to the nearest tenth. The base of the...

Geometry / Trig
What is the area of a regular hexagon with a distance from its center to a vertex of 1 cm? (Hint: A regular hexagon can be divided into six equilateral triangles.) hex The area of the regular hexagon is _____ ?

trig
Reiny 2+1/3*tan(theta)=2 How do you get 0? Thanks for your help.

Trig
2+1/3tan(theta)=2 I know that tan=0 0,180 But i don't know how to figure it out. Please help.

Trig
4=5+cos(theta)

Trig
Thank you Steve for all your help.

Trig
Solve equation for 0 less than or equal to theta less than 360. 3-1/5*tan(theta)=16/5

trig
Brian is riding a Ferris wheel. The wheel has a radius of 25 feet, and at his lowest point, Brian is 8 feet off the ground. Brian times how long it takes to travel from the lowest point to the highest point and finds that it takes 8 seconds. Write a sinusoidal equation to ...

Pre-cal/trig
A dog is attached to a 21​-foot rope fastened to the outside corner of a​ fenced-in garden that measures 18 feet by 22 feet. Assuming that the dog cannot enter the​ garden, compute the exact area that the dog can wander. I'm confused as to how they want me to solve this...

Trig
An isosceles triangle has a height of 12.5 m (measured from the unequal side) and two equal angles that measure 55°. Determine the area of the triangle. Split in half the triangle is a right triangle, so it's three angles are 90%, 55% and 70%. I'm still not sure how to find ...

Trig/PreCalc
Find a parametrization for the line segment with endpoints (5,2) and (-2, -4).

Trig/PreCalc
Use an algebraic method to eliminate the parameter and identify the graph of the parametric curve. x=5-3t y=2+t -1<-x-<3

Trig/PreCalc
Find the interior angles of the triangle with vertices (-4,1), (1,-6), and (5,-1)

Trig/PreCalc
An airplane is flying on a compass heading of 160 degrees at 425 mph. A wind is blowing with the bearing 200 degrees at 75 mph. Find the actual speed and direction of the airplane.

trig
A person is standing 90 feet away from the Space Needle. The person looks up at the Space Needle at an angle of elevation of 81 degrees. The distance from the floor to the person's eye level is 5 feet. What must be the height of the Space Needle?

Trig
Let n be a fixed positive integer. Describe all solutions of sin(n theta) = 1/2 I know that the solutions would be (π/6)/n+(2πx)/n and (5π/6)/n+(2πx)/n ? How do I 'describe'

Trig
Given: sin x = 4/5, 0 < x < π/2 sin y = 5/13, π/2 < y < π Find the exact value of sin(x + y) I presume I'm supposed to use the sum and difference formulas but I'm not sure how to get the exactly value of cos x or cos y

trig prove plz anyone help
Prove that: x - tan^-1(x) = tan^-1{(tanx - x)/(xtanx + 1)} plz help

Math - Trig / Pre - Calc
Standard form of hyperbola: Hyperbola: Vertices: (9,9), (9, -7) Foci: (9, 1 + 4 sqrt 13), (9, 1 - 4 sqrt 13)? Standard form Ellipse: vertices: (2 sqrt 10, -10), (-2 sqrt 10, -10) foci: (sqrt 30, -10), (-sqrt 30, -10)?

Math trig
Two towers 50 meters apart from the top of the shorter tower to the top of the taller tower 43 degree elevation, depression from the top of shorter tower to the bottom of the taller tower is 36 degrees what is the height of each tower?

Trig Question
Find solutions of the following equation which lie in the interval [0,2pi): 6cos(3theta)/(2)+3=0

Trig identities
Has a negative -5/13 Steve. If angles x and y are in the same quadrant and sin x =3/5 and cos y= -5/13 determine the value of sin (x-y)

Trig
Cicero has a population of 6200 people and is growing at a rate of 8% per year . Mattydale has a population of 8750 and is growing at a rate of 6% per year create and equation solve the problem and in how many years to the nearest year will Cicero have a greater population ...

trig
The rectangular coordinates of a point are given (0,-6). Find polar coordinates of the point such that r greater than 0 and 0 less than or equals theta less than 2pi. how to solve this damon please help me

trig
The rectangular coordinates of a point are given (-5,-5root3). Find polar coordinates of the point. Express theta in radians.

Math
Consider ∠C such that sin C = 7/25 a) What are the possible quadrants in which ∠C may lie? b) If you know that cos C is negative, how does your answer to part a) change? c) Sketch a diagram to represent ∠C in standard position, given that the condition in part b) is true...

Trig
What are the focus and directrix of the parabola represented by the equation:8(y-6)=(x+2)squared?

Trig
From a point A, 30 meters from the base of a building B, the angle of elevationto the top of the building C is 56 degrees. The angle of elevation to the top of flagpole D on top of the building is 60 degrees. Find the length of flagpole CD

Trig
Find the exact value of the trigonometric function given that sin u=3/5 and cos v=-8/17. Both u and v are in quadrant II. Tan (u+v)

Trig
find the angle between u=7i+2j and v=-4j

trig help
simplify cosec40(sin40+sin80+cos120) help step

trig help
simplify cosec40(sin40+sin80+cos120) help step

trig
A communication tower is 34m tall. Jane stands somewhere in front of the tower to the right and measures the angle of elevation to be 70 degrees. Bill stands somewhere in front of the tower to the left and measures the angle of elevation to be 50 degrees. How far apart are ...

Trig
find all solutions of 2sinx=1-2cosx in the interval from 0 to 360

Pre-Calc/ Trig
Find the sum of the three smallest positive values of theta such that 4(cos^2)(2theta-pi) =3. (Give your answer in radians.) LaTEX: Find the sum of the three smallest positive values of $\theta$ such that $4\cos^2(2\theta-\pi) =3$. (Give your answer in radians.)

Physics algebra and trig
A pair of fuzzy dice is hanging from the rearview mirror of a race car. As the car accelerates smoothly, the strings of the dice are tilted slightly toward the rear of the car. From the perspective of the driver, which one of the following statements is true, if the dice are ...

Trig
Write 3theta - sin 4theta as a product.

Trig
Use the half-angle formula to simplify (sin4theta)/(1+cos4theta)

math trig
how do you solve arcsin(3/5) without a calculator?

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