Question

For a particular angle Θ, the cosine function f(x) = a cos b(Θ) has the following values within one cycle of the function:

What is the rule for the cosine function?

Answer 1

If f(θ) = a cos(bθ), then from the first condition we find

f(0) = 3 ⇒ a cos(0) = 3 ⇒ a = 3

Together with the other conditions, it's evident that f(θ) has a period of π, so

2π/b = π ⇒ b = 2

so that

f(θ) = 3 cos(2θ)