document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1098976>Question 1098976</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all degree solutions in the interval 0° &#8804; &#952; < 360°. If rounding is necessary, round to the nearest tenth of a degree. Use your graphing calculator to verify the solution graphically. (Enter your answers as a comma-separated list.)<BR>\n" );
document.write( "4 sin^2 &#952; &#8722; 8 cos 2&#952; = 0<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 #713518 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=713518\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your equation is:\r<BR>\n" );
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document.write( "4 * sin^2(x) - 8 * cos(2x) = 0\r<BR>\n" );
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document.write( "x represents the angle theta.\r<BR>\n" );
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document.write( "add 8 * cos(2x) to both sides of this equation and you get:\r<BR>\n" );
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document.write( "4 * sin^2(x) = 8 * cos(2x)\r<BR>\n" );
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document.write( "cos(2x) is equal to cos^2(x) - sin^2(x)\r<BR>\n" );
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document.write( "cos^2(x) is equal to 1 - sin^2(x)\r<BR>\n" );
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document.write( "cos(2x) is therefore equal to 1 - sin^2(x) - sin^2(x).\r<BR>\n" );
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document.write( "this simplifies to cos(2x) = 1 - 2 * sin^2(x)\r<BR>\n" );
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document.write( "your equation becomes:\r<BR>\n" );
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document.write( "4 * sin^2(x) = 8 * (1 - 2 * sin^2(x))\r<BR>\n" );
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document.write( "simplify this to get 4 * sin^2(x) = 8 - 16 * sin^2(x)\r<BR>\n" );
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document.write( "add 16 * sin^2(x) to both sides of this equation to get:\r<BR>\n" );
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document.write( "20 * sin^2(x) = 8\r<BR>\n" );
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document.write( "divide both sides of this equation by 20 to get sin^2(x) = 8/20.\r<BR>\n" );
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document.write( "take the square root of both sides of this equation to get sin(x) = sqrt(8/20)\r<BR>\n" );
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document.write( "use your calculator to find the arcsin of sqrt(8/20).\r<BR>\n" );
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document.write( "you will find that the angle is equal to 39.23152048 degrees.\r<BR>\n" );
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document.write( "the equivalent angle in the second quadrant is 180 minus that.\r<BR>\n" );
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document.write( "the equivalent angle in the third quadrant is 180 plus that.\r<BR>\n" );
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document.write( "the equivalent angle angle in the fourth quadrant is 360 minus that.\r<BR>\n" );
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document.write( "the equivalent angles in each quadrant are therefore.\r<BR>\n" );
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document.write( "quadrant 1 = 39.23152048<BR>\n" );
document.write( "quadrant 2 = 140.7684795<BR>\n" );
document.write( "quadrant 3 = 218,2315295<BR>\n" );
document.write( "quadrant 4 = 320.7684795\r<BR>\n" );
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document.write( "you want to check that 4 * sin^2(x) = 8 * cos(2x) = 0 for each of these angles.\r<BR>\n" );
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document.write( "quadrant 1 = 0<BR>\n" );
document.write( "quadrant 2 = 0<BR>\n" );
document.write( "quadrant 3 = 0<BR>\n" );
document.write( "quadrant 4 = 0\r<BR>\n" );
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document.write( "the formula checks out ok in all 4 quadrants, therefore your solution is the angles in each of the quadrant.\r<BR>\n" );
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document.write( "this is confirmed by the following graph of y = 4 * sin^2(x) and y = 8 * cos(2x).\r<BR>\n" );
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document.write( "the intersection of these 2 equations is your solution and it confirms that the angle in each of those quadrants provides the correct solution.\r<BR>\n" );
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document.write( "here's the graph.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/102621.jpg\" alt=\"$$$\" ><BR>\n" );
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