Question 1202129
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The period of g is 2pi, and the period of f is half the period of g, so the period of f is pi.<br>
f(0) and g(0) are both zero, so theta=0 is the beginning of a period for both f and g.<br>
Since theta = 0 is the beginning of a period for f, which has a period of pi, theta = pi/4 is 1/4 of the way through a period.  A sine function is at its maximum 1/4 of the way through a period, so the maximum value of f is f(pi/4)=4.<br>
That means the amplitude of f is 4; and since the amplitude of f is twice the amplitude of g, the amplitude of g is 2.<br>
So g has ampitude 2 and period 2pi; the function is g = 2sin(theta).<br>
ANSWER: g = 2sin(theta)<br>