Question

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

Answer 1

Hi :)

Answer 2

Initial data tells us that there is no horizontal or vertical shift,
\(\large\rm f(0)=g(0)=0\)

amplitude of f is twice amplitude of g,
\(\large\rm A_f=2A_g\)

Answer 3

Period of f is half that of period of g,
\(\large\rm P_f=\frac12P_g\)

They tell us that the period of g is 2pi,
\(\large\rm P_f=\frac12(2\pi)\)
so the period for our f function is just pi, ya?

Answer 4

Let's think about how that helps us...
recall that the period is related to the b coefficient from this standard form:
\(\large\rm y(x)=A\sin(bx)\)

And it's related in this way: \(\large\rm b=\frac{2\pi}{P}\)
So if we divide 2pi by this period value that we've found,
we can determine the b value for our function f.