Question

The difference in length of a spring on a pogo stick from its non-compressed length when a teenager is jumping on it after θ seconds can be described by the function f of theta equals 2 times sine theta plus radical 3 periodPart C: A toddler is jumping on another pogo stick whose length of their spring can be represented by the function g of theta equals 1 minus cosine squared theta plus radical 3 period At what times are the springs from the original pogo stick and the toddler's pogo stick lengths equal?

Answer 1

C)

g(θ) = 1 - cos^θ + √3

Recall, Sin^2θ = 1 - Cos^2θ. Thus,

g(θ) = Sin^2θ + √3

g(θ) = f(θ)

Sin^2θ + √3 = 2Sinθ + √3

Sin^2θ = 2Sinθ + √3 - √3

Sin^2θ = 2Sinθ

Sin^2θ - 2Sinθ = 0

By factoring Sinθ, we have

Sinθ(Sinθ - 2) = 0

Sinθ = 0 or Sinθ - 2 =

Sinθ = 0 or Sin