document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=921246>Question 921246</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help!<BR>\n" );
document.write( "The graph of one complete period of a sine and cosine curve is given.?<BR>\n" );
document.write( "please explain how to fill out these graphs thank you \r<BR>\n" );
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document.write( "http://i.imgur.com/rCXQUym.png <BR>\n" );
document.write( "http://i.imgur.com/X1cZq8F.png </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #558884 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=558884\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your first picture is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/110702a.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "the interval goes from 0 to 4p/4 which is the same as from 0 to pi.\r<BR>\n" );
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document.write( "the period is therefore equal to pi.\r<BR>\n" );
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document.write( "the frequency is equal to 2pi / pi = 2\r<BR>\n" );
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document.write( "there is no phase shift because cosine = 1 at 0 radians which is the value shown on the graph.\r<BR>\n" );
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document.write( "the equation in the form of y = a * cos (k(x-b)) becomes:\r<BR>\n" );
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document.write( "y = 6 * cos(2 * x)\r<BR>\n" );
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document.write( "i graphed it to confirm.\r<BR>\n" );
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document.write( "that graph is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/110702b.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "you can see the equation on the top left.\r<BR>\n" );
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document.write( "the graph matches your picture so it looks good.\r<BR>\n" );
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document.write( "your second picture is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/110703a.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "the amplitude is 6.\r<BR>\n" );
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document.write( "the interval goes from -3/4 to 1/4.\r<BR>\n" );
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document.write( "the period is therefore equal to 1.\r<BR>\n" );
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document.write( "the frequency is equal to 2pi / 1 = 2pi.\r<BR>\n" );
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document.write( "the sine wave should be 0 when x = 0.\r<BR>\n" );
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document.write( "this sine wave appears to be shifted to the right by 1/4 of the period.\r<BR>\n" );
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document.write( "the phase shift is therefore equal to 1/4.\r<BR>\n" );
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document.write( "the equation in the form of y = a * sin (k * (x-b)) becomes:\r<BR>\n" );
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document.write( "y = 6 * sin(2pi * (x-1/4))\r<BR>\n" );
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document.write( "the graph of that equation is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/110703b.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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