The functions f(θ) and g(θ) are sine functions, where f(0) = g(0) = 0.

Question

The amplitude of f(θ) is twice the amplitude of g(θ). The period of f(θ) is one-half the period of g(θ). If g(θ) has a period of 2pi and f (pi/4) = 4, write the function rule for g(θ).

Answer 1

g(θ) has a period of 2π means:
g(θ) = a sin(θ)

The amplitude of f(θ) is twice the amplitude of g(θ).
The period of f(θ) is one-half the period of g(θ).
means:
f(θ) = 2a sin(2θ)

f(π/4) = 2a sin(π/2) = 2a = 4, so a=2
g(θ) = 2sin(θ)