document.write( "Question 1202129: 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.
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #836773 by ikleyn(52858) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "The functions f(theta) and g(theta) are sine functions, where $\"highlight%28cross%28f%28theta%29=g%28theta%29=0%29%29\"$ f(0) = g(0) = 0.
\n" ); document.write( "The amplitude of f(theta) is twice the amplitude of g(theta).
\n" ); document.write( "The period of f(theta) is one-half the period of g(theta).
\n" ); document.write( "If g(theta) has a period of 2pi and f(pi/4)=4. Write the function rule for g(theta).
\n" ); document.write( "Explain your reasoning.
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "        Notice that I changed/edited your post \r
\n" ); document.write( "\n" ); document.write( "        by guiding my common sense and the context.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "        Also, in this situation, there is no need to torture yourself, writing \"theta\" everywhere,\r
\n" ); document.write( "\n" ); document.write( "        when it is possible to replace it by short variable \"x\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "According to the problem, functions g(x) is sinusoidal, has the value of 0 at x= 0 \r\n" );
document.write( "and has a period  . Hence, g(x) has the form\r\n" );
document.write( "\r\n" );
document.write( "    g(x) = ,  where real number \"b\" is the amplitude of g(x).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Function f(x) is sinusoidal, has the value of 0 at x= 0 and has a period, which is \r\n" );
document.write( "one-half of that of g(x), i.e. . Hence, f(x) has the form\r\n" );
document.write( "\r\n" );
document.write( "    f(x) = ,  where real number \"a\" is the amplitude of f(x).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Next,  we are given   = 4.  It means    = 4,  or   = 4.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Since   = 1,  it gives us  a = 4.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It implies, due to the problem description, that the amplitude of  g(x)  is  2 :  b = 2.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus g(x) has the form\r\n" );
document.write( "\r\n" );
document.write( "     g(x) = .    ANSWER\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );