document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=388313>Question 388313</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Using f(x)=1sin x or f(x)=cos x as a guide,graph each function. Identify the amplitude and the period.\r<BR>\n" );
document.write( "\n" );
document.write( "f(x)=2 sin 1/2 x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "thnxs </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #274616 by </B><A HREF=/tutors/aboutme.mpl?userid=texttutoring><B>texttutoring(324)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=texttutoring><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=texttutoring><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=274616\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The sine graph will look like this: http://www.wolframalpha.com/input/?i=y%3D2+sin(x/2)\r<BR>\n" );
document.write( "\n" );
document.write( "(Copy and paste the URL if you can't click it.)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In any sine curve, the general equation is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y=a*sinb(x-c) + d\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Where a=amplitude, b=compression (determines period), c=phase shift (left or right shift), and d=vertical displacement (up/down shift)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In your question, a=2, b=1/2, and c=0, d=0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the amplitude is 2. This means that the curve goes up to a max of y=2 and a min of y=-2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You can find the period by using this simple formula:\r<BR>\n" );
document.write( "\n" );
document.write( "P = 2Pi /b\r<BR>\n" );
document.write( "\n" );
document.write( "Your value of b is 1/2, so the period is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "P = 2Pi / (1/2)<BR>\n" );
document.write( "P = 4Pi\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the period of this function is 4Pi, which you should be able to see from the graph on the link. In essence, this means that the curve was stretched out in the x-direction by double. If b=2, it would be compressed to a period of 1Pi.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Hope this helps! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );