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Trigonometry

Proving Trigonometric Identities (5 Problems)

Prove the following identities..."not an identity" is an option. Please explain in detail and in steps how to perform the following: 1. cot²x-cos²x=cos²xcot²x 3. tanx= square rt of sec²x-1 4. sinx/1-cotx + cosx/1-tanx=cosx+sinx 5. cotx-1/1-tanx = cscx/secx 6. cosxsiny=1/2(sin(x+y)-sin(x-y)

Inverse Functions

Find the exact value of the expression(Consider interval is [0,pi] I) 1) sin^-1 SQRT3 / 2 = pi/3 2) arctan(-1) = 3pi / 4 3) csc^-1 2 = pi/6 4) sec^-1 SQRT(2) = pi/4 II) We were given the example to derive sin^-1x as follows. y=sin^-1 (x) siny = x (cosy)(dy/dx) = 1 (dy/dx) = 1/cosy = 1 / (SQRT(1-sin^2 (y)) = 1

Right triangle trigonometry college algebraic

A. As a group, work together to submit the answers to the following problems. Use the Small Group Discussion Board to divide tasks, discuss strategies for solving problems, and check each other's work. The finished product should be one combined document for the entire group, showing all calculations and graphical representat

Trigonometric Identities

43. Express cos 3 in terms of cos x. ans. cos3x=4cos^3x-3cosx 47. 2 cos 2y sin 2 y ans. sin 4y 51. sin 16x = 2 sin 8 x cos 8x ans. sin 16x=sin (2(8x))= 2 sin 8x cos 8x 55.cos 4x=2cos2x-1 ans. not an identity

Travel in Kilometers

Suppose you travel north for 35 kilometers then travel east 65 kilometers. How far are you from your starting point? Can you show me how you got the answer?

Initial Value problem

Could someone help me with the problem and provide all the steps please. y'' + 4y' + 5y = 35e^(-4x) y(0)=-3, y'(0)=1

Find all solutions to the given trigonometric equation.

Find all solutions of the equation Sec^2-2=0 The answer is A+B(k)(pi) where k is any integer and 0<A<pi/2, A= B= I have one answer as pi/4 for A that is correct, but I cannot figure out how to get B. I was using +-sqrt2/2 to get the A answer.

Geometric Constructions

See attached pdf file. The Trig identities you might need are 2cos^2 (x) - cos(2x) - 1=0 and 4cos^3(x) - 3cos(x)=0

Trigonometry equation

S=4sin(t+^0) with a force acting upon it P=7sin(t-39) If E at time t is ps and E=-14cos(2t-60) How do you arrive at this.

Trigonometry Equation

What is the process to determine a force acting upon a body as in a displacement represented by say p=?sin(t+?degree) with a force say n =?sin(t-?degrees) so that it evaluates to a given figure of energy of motion?

Tan (2 arc cos (x/3))

Simplify: tan (2 arc cos (x/3)) Solution shall not contain trig and inverse trig functions. Do not use calculator.

Solve Trigononmetric Expressions (8 Problems) ( Arcsin and Arccos )

Set -pi/2 <= x <= pi x = arcsin[sin(5pi/3)] = _______pi x = arcsin[sin(7pi/4)] = _______pi x = arccos[cos(-5pi/6)] = ______pi x = arccos[cos(3pi/2)] = _______pi x = arccos[cos(3pi/4)] = ______pi x = arctan[cos(3pi/2)] = ______pi x = arcsin[sin(7pi/6)] = _____pi Write as a multiple of pi. pi = 3.14159.

Review of previous posting

(See attached file for full problem description and diagrams) --- Need help with the following questions. A Little League team is building a backstop for its practice field. It is made up of two right angles as shown below. The backstop extends 24 feet 8 inches out in each direction and the center pole is 6.5 yards high.

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

Amplitude

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