# Trigonometry

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

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?

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)