document.write( "Question 888977: given that tan theta=7/24 withtheta in quadrant 3 find sin 2 theta \n" ); document.write( "
Algebra.Com's Answer #537805 by Theo(13342)\"\" \"About 
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tan(theta) = 7/24
\n" ); document.write( "tan is equal to sin/cos.
\n" ); document.write( "since the angle is in quadrant 3, sine and cos are minus.
\n" ); document.write( "this makes tan(theta) = -7/-24.
\n" ); document.write( "use the quadratic formula to find the hypotenuse which is equal to 25.
\n" ); document.write( "couple of ways to solve this.
\n" ); document.write( "first way is to use the sin(2T) formula.
\n" ); document.write( "that formula says sin(2T) = 2 * sin(T) * cos(T).
\n" ); document.write( "sin(T) = -7/25
\n" ); document.write( "cos(T) = -24/25
\n" ); document.write( "2 * sin(T) * cos(T) = 2 * -7/25 * -24/25 which is equal to -336 / 625 which has a decimal equivalent of .5376.
\n" ); document.write( "second way is to find the angle and then double it and then take the sign of that doubled angle.
\n" ); document.write( "since tan(theta) = 7/24, use your calculator to find theta = 16.26020471.
\n" ); document.write( "that's in the first quadrant.
\n" ); document.write( "in the third quadrant, the angle is 180 + 16.26020471 = 196.26020471.
\n" ); document.write( "double that to get 392.5204094.
\n" ); document.write( "use your calculator to get sin(392.5204094) = .5376
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