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Be sure to show and explain all work. 10 points each Part 1 - Application A mass oscillating up and down on the bottom of a spring (assuming perfect elasticity and no friction or air resistance) can be modeled as harmonic motion. If the weight is displaced a maximum of 6 cm, nd the modeling equation if it takes 4 seconds to complete one cycle. Be to show, illustrate and explain your work. Part 2 - Find the error(s) and solve the problem correctly. Be sure to explain and show your work. Where did the "wrong answer" come from? Sin 52 Answer: sin 52 = .9866 Part 3 - Discussion Question Name 4 other angles whose cosine is the same as cos %. Explain using mathematical language how you know this is true. (calculations only using a calculator is not considered mathematical language). Is this statement true or false? Explain your answer. Ail angles that have the same cosine will have the same sine. Part 1 - Application Find your own values that prove that tan(u-v) # tan u - tan v. Show your work and explain why you chose these values. Part 2 - Find the error(s) and solve the problem correctly. Explain your corrections. Solve: 2cos x = 4 cos x sin x Answer: 2cos x = 4 cos x sin x 2cos x = 4 cos x sin x (2 cos x in common onboth sides) 1 = sin x The only place sin x = 1 is where the angle is ,. x = Part 3 - Discussion Question Is it possible to factor 1 - sin x two different ways? If so, show and explain. If not, why not?. Factor the algebraic expression below in terms of a single trigonometric function. cos x - sin 2x - 1 (2 points) Find all solutions to the equation. cos x + 2 cos x + 1 = 0 (4 pointsVerify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation. 1. cot x sec4X = cot x + 2 tan x + tan3x 2. (sin x)(tan x cos x - cot x cos x) = 1 - 2 cos2x 3. 1 + sec2x sin2x = sec2x sin x sin x . 1- COS X + 1+ Cosx = 2 CSC X 5. - tan2x + sec2x = 1Write the expression as either the sine, cosine, or tangent of a single angle. (2 points) COs cos + sin sinFind the exact value by using a half-angle identity. (4 points) 7n sin 8\fVerify the identity. (8 points 1 - sin x COS X COS X 1+ sin xVerify the identity. (7 points COS X+ = -sin x