Somebody, please help

The functions f(_) and g(_) are sine functions, where f(0) = g(0) = 0. The amplitude of f(_) is twice the amplitude of g(_). The period of f(_) is one-half the period of g(_). If g(_) has a period of 2pi and f (pi/4) = 4, write the function rule for g(_).

Respuesta :

f(x) can be written as:
f(x) = Asin(2x); where A is the amplitude and the period of the function is half that of a normal sin function.
f(π/4) = 4
4 = Asin(2(π/4))
4 = Asin(π/2)
A = 4
Amplitude of g(x) = 1/2 * amplitude of f(x)
A for g(x) = 2
g(x) = 2sin(x)