document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202129>Question 1202129</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The functions f(theta) and g(theta) are sine functions, where f(theta)=g(theta)=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). Explain your reasoning.<BR>\n" );
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document.write( "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><BR>\n" );
document.write( "f(0) and g(0) are both zero, so theta=0 is the beginning of a period for both f and g.<br><BR>\n" );
document.write( "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><BR>\n" );
document.write( "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><BR>\n" );
document.write( "So g has ampitude 2 and period 2pi; the function is g = 2sin(theta).<br><BR>\n" );
document.write( "ANSWER: g = 2sin(theta)<br><BR>\n" );
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