Trigonometry Problem

Question

Let f(θ)= cosθ, and g(θ)= 3f(1/2θ).

On the interval θ∈[0,2π], explain how the coordinates of the x- and y-intercepts of g are obtained from the coordinates of the x- and y-intercepts of f. Use exact values in your response.

Answer 1

g(θ) = 3 cos (θ / 2)

The 3 affects the amplitude, not the x-intercepts.

cos θ has x-intercepts at π/2 + kπ

cos θ/2 has x-intercepts π/4 + kπ and 3π/4 + kπ

Draw and label the graphs.