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Trigonometry: Close Encounters of the Third Kind

In the movie Close Encounters of Third Kind, there was a scene where the star, Richard Dreyfuss, was approaching Devil's Tower in Wyoming. He could have determined his distance from Devil's Tower by first stopping at point P, and taken a measurement of the angle from his location to the height of the tower of 13.5 degrees. He


What is the amplitude of the wave of the equation y=-4 sin 5x?

Spherical polar coordinates

I am trying to find the grad function of the spherical polar coordinates shown on the attached file. I have completed the question to a certain extent but am not sure if it is correct. Could you please ensure its accuracy and complete by simplifying the solution (trig identities etc) as I am unable to do so? (See attached f

Tangent sum formulas

Explain why tan(x + 450 degrees) cannot be simplified using the tangent sum formulas but can be simplified by using the sine and cosine formulas. (Please show all work).

15 Trigonometry Problems : Angular Velocity, Shadows, Waves and Triangles

Trigonometry Review 1. Assume the angle of inclination of the sun is given by Theta = (pi/12)t, where t is the number of hours after sunrise. Suppose we have a 10 meter high flagpole. a. What is the angular velocity of the sun? b. Write an equation for the length of the flagpole's shadow when the angle of the sun is theta rad

Wave Equation : Triangular Pulse

Let u(x; y) be the solution on 0 < x < 2 and 0 < y < 2 of uxx + uyy = 0 with u(0, y) = u(2, y) = u(x, 2) = 0 and u(x, 0) = f(x) the triangular pulse with f(0) = f(2) = 0 and f(1) = 2. f(x) = {2x 0<x<1 {-2x+4 1<x<2 Let uj,k = u(j/2; k/2) for j = 1; 2; 3 and k = 1; 2; 3 as obtained by the numerical method. (a)

Trigonometric Substitution

Please see the attached file for the fully formatted problem. Use trigonometric substitution to write the algebraic expression sqrt(36-4x2) as a trigonometric function, where the substitution is x = 3 cos theta and 0<theta<pi/2.

Trigonometric equation

See attached file --- find all solutions of the equation in the interval [0,2&#61552;). tan(x+ pi) + 2sin(x+pi) = 0 [show all the steps in solving this equation, not just the answer] ---

10 Trigonometry Application Word Problems : Angles and Lengths

1. Suppose that a boat leaves Jacksonville traveling at a bearing of 110o. It goes 30.0 km, and then travels 100.0 km at a bearing of 170o. How far is it from Jacksonville? 2. Suppose that I am trying to judge the distance across a lake. I stand facing some house on the opposite shore. I turn 95o to the left, and walk 20 me

Half and quarter range sine and cosine expansion

Please show each step of your solution. When you use theorems, definitions, etc., please include in your answer. 6. In each case solve (1) with boundary conditions (1b) changed as indicated, and for the specified f(x). Use a half- or quarter-range cosine or sine expansion, as appropriate... Please see attached.

Solving Trigonometric Equations

Solve each equation for exact solutions in the interval [0, 360]. Use either an algebraic method or a graphical method. 2 sin x -1 = csc x

Proving Trigonometric Identities

Prove sec 2A + tan 2A = (cos A + sin A)/ (cos A - sin A) Express this as a sum of 2 trigo functions 2(siny)(sin5y) Prove (sin2A)^2 - (sinA)^2 = (sinA)(sin3A)

Related Rates and Trigonometry : Rate of Rotation of a Searchlight

A man walks along a straight path at a speed of 4 ft/s. A searchlight is located on the ground 20 ft from the path and is kept focused on the man. At what rate is the searchlight rotating when the man is 15 ft from the point on the path closest to the searchlight?