document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1083715>Question 1083715</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use a reference rectangle and the rule of fourths to draw an accurate sketch of the following function through at least one full cycle.<BR>\n" );
document.write( "y = cos(4t) <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #697793 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=697793\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y = cos(4t) has a frequency of 4.\r<BR>\n" );
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document.write( "period = 2pi / frequency = 2pi / 4 = 2pi/4 = pi/2.\r<BR>\n" );
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document.write( "the full cycle of the cosine function of y = cos(4t) goes from 0 to pi/2.\r<BR>\n" );
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document.write( "if you break the period into quarters, you will get quarter periods of pi/2 / 4 = pi/8.\r<BR>\n" );
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document.write( "the function starts at x = 0<BR>\n" );
document.write( "the first quarter ends at pi/8<BR>\n" );
document.write( "the second quarter ends at 2pi/8<BR>\n" );
document.write( "the third quarter ends at 3pi/8<BR>\n" );
document.write( "the fourth quarter ends at 4pi/8\r<BR>\n" );
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document.write( "simplify the fractions and you get:\r<BR>\n" );
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document.write( "the function starts at x = 0<BR>\n" );
document.write( "the first quarter ends at pi/8<BR>\n" );
document.write( "the second quarter ends at pi/4<BR>\n" );
document.write( "the third quarter ends at 3pi/8<BR>\n" );
document.write( "the fourth quarter ends at pi/2\r<BR>\n" );
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document.write( "your rectangle has vertical sides at x = 0 and x = pi/2.\r<BR>\n" );
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document.write( "your rectangle has horizontal sides at y = 1 and y = -1.\r<BR>\n" );
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document.write( "here's the graph of cos(4x).\r<BR>\n" );
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document.write( "x is used instead of 5 to satisfy the graphing software.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/060406.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "here's a reference on graphing of sine and cosine functions.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.purplemath.com/modules/grphtrig.htm\" target =\"_blank\">http://www.purplemath.com/modules/grphtrig.htm</a>\r<BR>\n" );
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