document.write( "Question 1155044: find the exact value of cos(2θ)and sin(2θ) if tan(θ) = (-5/12) and 270° < θ < 360° \n" ); document.write( "

Algebra.Com's Answer #777599 by Edwin McCravy(20056) $\"\"$ $\"About$

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document.write( "We know that  270° < θ < 360° means that θ is in quadrant IV.\r\n" );
document.write( "We also know that the tangent is the opposite/adjacent or y/x.\r\n" );
document.write( "So we can draw a right triangle in the 4th quadrant so that\r\n" );
document.write( "the opposite side is the numerator +5 of the tangent (-5/12) \r\n" );
document.write( "taken as (+5)/(-12), and the denominator is -12 of the tangent \r\n" );
document.write( "taken as (+5)/(-12).  So we have the drawing: \r\n" );
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document.write( "Next we use the Pythagorean theorem to calculate r:\r\n" );
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document.write( "Fill in the value of r=13:\r\n" );
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document.write( "Now we use the formula for sin(2θ):\r\n" );
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document.write( "and the fact that the sine is opposite/hypotenuse or y/r = (-12)/(13) = -12/13\r\n" );
document.write( "and the fact that the cosine is adjacent/hypotenuse or x/r = (+5)/(13) = 5/13\r\n" );
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document.write( "We use the formula for cos(2θ):\r\n" );
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document.write( "Edwin

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