document.write( "Question 1174752: Use an identity to evaluate sin2θ when the angle, θ terminates in quadrant III and tanθ=4/3. (I am sure I need to use the identity sin(2θ) = 2 sinθ cosθ, but I am unsure how use this for tan) \n" ); document.write( "
Algebra.Com's Answer #800247 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
you are given that tan(theta) = 4/3.\r
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\n" ); document.write( "\n" ); document.write( "to find the angle, solve for arctan(4/3) using your calculator.
\n" ); document.write( "you will find that arctan(4/3) = 53.13010235 degrees.\r
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\n" ); document.write( "\n" ); document.write( "that's the angle in the first quadrant.
\n" ); document.write( "the equivalent angle in the third quadrant is 180 + 53.13010235 = 233.13010235 degrees.\r
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\n" ); document.write( "\n" ); document.write( "you are now looking for sin(2 * theta) when theta = 233.13010235 degrees.
\n" ); document.write( "2 * theta = 466.2602047 degrees.
\n" ); document.write( "you get sin(2 * 233.13010235) = sin(466.2602047)) = .96.
\n" ); document.write( "that should be your answer.\r
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\n" ); document.write( "\n" ); document.write( "if you used the sin(2 * theta) identity, you would have gotten:
\n" ); document.write( "sin(2 * theta) = 2 * sin(theta) * cos(theta) which becomes:
\n" ); document.write( "sin(2 * theta) = 2 * sin(233.13010235) * cos(233.13010235) = .96.\r
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\n" ); document.write( "\n" ); document.write( "that's the same as we got before, so it should be good.\r
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