document.write( "Question 1036142: Find sin 2 theta, cos 2 theta, and tan 2 theta for each set of conditions.\r
\n" ); document.write( "\n" ); document.write( "cos theta = -5/13 and pi/2 < theta < pi.\r
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Algebra.Com's Answer #650772 by ikleyn(52794)\"\" \"About 
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\n" ); document.write( "Find sin 2 theta, cos 2 theta, and tan 2 theta for each set of conditions.\r
\n" ); document.write( "\n" ); document.write( "cos theta = -5/13 and pi/2 < theta < pi.
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document.write( "Since  \"cos%28theta%29\" = \"-5%2F13\"  and  \"pi%2F2\" < \"theta\" < \"pi\", \r\n" );
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document.write( "\"sin%28theta%29\" = \"sqrt%281+-+%28-5%2F13%29%5E2%29\" = \"sqrt%281+-+25%2F169%29\" = \"sqrt%28%28169-25%29%2F169%29\" = \"sqrt%28144%2F169%29\" = \"12%2F13\".\r\n" );
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document.write( "The sign \"+\" was chosen at the square root because the sine is positive in the second quadrant.\r\n" );
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document.write( "Next,\r\n" );
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document.write( "\"sin%282%2Atheta%29%29\" = \"2%2Asin%28theta%29%2Acos%28theta%29\" = \"2%2A%2812%2F13%29%2A%28-5%2F13%29%29\" = \"-120%2F169%29\",\r\n" );
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document.write( "\"cos%282%2Atheta%29%29\" = \"cos%5E2%28theta%29+-+sin%5E2%28theta%29\" = \"%28-5%2F13%29%5E2+-+%2812%2F13%29%5E2\" = \"25%2F169+-+144%2F169\" = \"-119%2F169\".\r\n" );
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document.write( "By the way, the signs of the  \"sin%282theta%29\"  and  \"cos%282theta%29\"  say  that \"2theta\"  lies in the quadrant 3.\r\n" );
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document.write( "Now,  \"tan%282%2Atheta%29\" = \"sin%282%2Atheta%29%2Fcos%282%2Atheta%29\" = \"%28%28-120%2F169%29%29%2F%28%28-119%2F169%29%29\" = \"120%2F119\".\r\n" );
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document.write( "Solved.\r\n" );
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