document.write( "Question 748758: Find the exact values of sin 2a, cos 2a, and tan 2a.
\n" ); document.write( "tan a=2, pi < a < 3pi/2 \n" ); document.write( "
Algebra.Com's Answer #455644 by lwsshak3(11628)\"\" \"About 
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Find the exact values of sin 2a, cos 2a, and tan 2a.
\n" ); document.write( "tan a=2, pi < a < 3pi/2
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\n" ); document.write( "tan(a)=2
\n" ); document.write( "hypotenuse=√(2^2+1)=√5
\n" ); document.write( "sin(a)=-2/√5
\n" ); document.write( "cos(a)=-1/√5
\n" ); document.write( "..
\n" ); document.write( "sin(2a)=2sin(a)cos(a)=2*-2/√5*-1/√5=4/5
\n" ); document.write( "cos(2a)=cos^2(a)-sin^2(a)=1/5-4/5=-3/5
\n" ); document.write( "tan(2a)=(2tan(a))/(1-tan^2(a))=4/(1-4)=-4/3
\n" ); document.write( "..
\n" ); document.write( "computer check:
\n" ); document.write( "tan(a)=2
\n" ); document.write( "a=243.13º (in quadrant III)
\n" ); document.write( "2a=486.86º-360=126.86º(in quadrant II)
\n" ); document.write( "reference angle=126.86-180=53.13º
\n" ); document.write( "..
\n" ); document.write( "sin(2a)=sin(53.1º)≈0.799...
\n" ); document.write( "exact value=4/5=0.800
\n" ); document.write( "..
\n" ); document.write( "cos(2a)=cos(53.1º)≈-0.600...
\n" ); document.write( "exact value=-3/5=-0.600
\n" ); document.write( "..
\n" ); document.write( "tan(2a)=tan(53.1º)≈-1.331...
\n" ); document.write( "exact value=-4/3=-1.333... \n" ); document.write( "
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