document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=884056>Question 884056</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2cos%5E2%28x%29=sin%5E2%28x%29 ALIGN=MIDDLE  ALT=\"2cos%5E2%28x%29=sin%5E2%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3C=x%3C=360 ALIGN=MIDDLE  ALT=\"0%3C=x%3C=360\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #533969 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=533969\">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( "2cos^2(x) = sin^2(x)\r<BR>\n" );
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document.write( "since cos^2(x) = 1 - sin^2(x), your equation becomes:\r<BR>\n" );
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document.write( "2 * (1 - sin^2(x)) = sin^2(x)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "2 - 2*sin^2(x) = sin^2(x)\r<BR>\n" );
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document.write( "add 2*sin^2(x) to both sides of the equation to get:\r<BR>\n" );
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document.write( "2 = sin^2(x) + 2*sin^2(x) which results in:\r<BR>\n" );
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document.write( "2 = 3*sin^2(x)\r<BR>\n" );
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document.write( "divide both sides of this equation by 3 to get:\r<BR>\n" );
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document.write( "2/3 = sin^2(x)\r<BR>\n" );
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document.write( "take the square root of both sides of this equation to get:\r<BR>\n" );
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document.write( "sin(x) = plus or minus sqrt(2/3)\r<BR>\n" );
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document.write( "take the arcsin of sqrt(2/3) to get:\r<BR>\n" );
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document.write( "x = 54.73561032 degrees.\r<BR>\n" );
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document.write( "take the arcsin of - sqrt(2/3) to get:\r<BR>\n" );
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document.write( "x = - -54.73561032 degrees.\r<BR>\n" );
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document.write( "the sine is positive in quadrant 1 and 2.\r<BR>\n" );
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document.write( "the angle in quadrant 1 is 54.73561032 degrees.<BR>\n" );
document.write( "the angle in quadrant 2 is 180 - 54.73561032 which is equal to 125.2643897 degrees.\r<BR>\n" );
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document.write( "the sine is negative in quadrant 3 and 4.\r<BR>\n" );
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document.write( "the angle in quadrant 3 is 180 + 54.73561032 which is equal to 234.7356103 degrees.\r<BR>\n" );
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document.write( "the angle in quadrant 4 is 360 - 54.73562032 which is equal to 305.2643897.\r<BR>\n" );
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document.write( "note that an angle of 305.2643897 degrees is the same angle as - 54.73561032 degrees, i.e. they are the identical position on the standard trig function graph.\r<BR>\n" );
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document.write( "confirm your answer is correct by substituting in the original equation for x.\r<BR>\n" );
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document.write( "your original equation is:\r<BR>\n" );
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document.write( "2cos^2(x) = sin^2(x)\r<BR>\n" );
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document.write( "when x = 54.73561032 degrees:\r<BR>\n" );
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document.write( "sin^2(x) = 2/3<BR>\n" );
document.write( "2cos^2(x) = 2/3<BR>\n" );
document.write( "they are equal.\r<BR>\n" );
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document.write( "when x = 125.2643897 degrees:\r<BR>\n" );
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document.write( "sin^2(x) = 2/3<BR>\n" );
document.write( "2cos^2(x) = 2/3<BR>\n" );
document.write( "they are equal.\r<BR>\n" );
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document.write( "when x = 234.7356103 degrees:\r<BR>\n" );
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document.write( "sin^2(x) = 2/3<BR>\n" );
document.write( "2cos^2(x) = 2/3<BR>\n" );
document.write( "they are equal.\r<BR>\n" );
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document.write( "when x = 305.2643897 degrees:\r<BR>\n" );
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document.write( "sin^2(x) = 2/3<BR>\n" );
document.write( "2cos^2(x) = 2/3<BR>\n" );
document.write( "they are equal.\r<BR>\n" );
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document.write( "a graph of both equations is shown below:<BR>\n" );
document.write( "you can see on the graph that the equation of sin^2(x) intersects with the equation of 2cos^2(x) at the indicated spots on the graph which is equal to y = 2/3 in all cases.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/jun2405.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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