document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=971541>Question 971541</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve on the interval [0, 2pi]\r<BR>\n" );
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document.write( "2cos*2x=1<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 #594060 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=594060\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> we'll do this in degrees and then translate to radians.\r<BR>\n" );
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document.write( "it's easier to show.\r<BR>\n" );
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document.write( "cos(2x) = .5\r<BR>\n" );
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document.write( "find cos^-1(.5) and you get 2x = 60 degrees.\r<BR>\n" );
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document.write( "that means that x is equal to 30 degrees.\r<BR>\n" );
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document.write( "the period of x is equal to 180 degrees because the frequency of x is equal to 2.\r<BR>\n" );
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document.write( "within that period of 180 degrees, you have 4 quadrants.\r<BR>\n" );
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document.write( "cosine is positive in the first and fourth quadrant.\r<BR>\n" );
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document.write( "30 degrees is in the first quadrant.\r<BR>\n" );
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document.write( "180 - 30 = 150 degrees is in the fourth quadrant.\r<BR>\n" );
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document.write( "within a 360 degree interval, you will get two full cycles of cosine(2x).\r<BR>\n" );
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document.write( "the cosine will be .5 at 30, 150, 30 + 180, 150 + 180.\r<BR>\n" );
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document.write( "that equates to 30, 150, 210, 330 degrees.\r<BR>\n" );
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document.write( "i'll show you the graph in degrees and then translate to radians.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/052101.jpg\" alt=\"$$$\" </a>\r<BR>\n" );
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document.write( "here's the same graph in radians.<BR>\n" );
document.write( "look under the graph for further comments.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/052103.jpg\" alt=\"$$$\" </a>\r<BR>\n" );
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document.write( "instead of an interval from 0 to 360, you have an interval from 0 to 2pi.\r<BR>\n" );
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document.write( "conversion factor from degress to radians is radians = degrees * pi / 180.\r<BR>\n" );
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document.write( "30 degrees would be equal to 30/180 * pi which is equal to pi/6.\r<BR>\n" );
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document.write( "150 degrees would be equal to 150/180 * pi which is equal to 5pi/6.\r<BR>\n" );
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document.write( "210 degrees would be equal to 210/180 * pi which is equal to 7pi/6.\r<BR>\n" );
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document.write( "330 degrees would be equal to 330/180 * pi which is equal to 11pi/6.\r<BR>\n" );
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