document.write( "Question 961906: find the exact values of sin 2a, cos 2a, and tan 2a when tan a = 2, π < a < 3π/2 \n" ); document.write( "
Algebra.Com's Answer #587694 by lwsshak3(11628)\"\" \"About 
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find the exact values of sin 2a, cos 2a, and tan 2a when tan a = 2, π < a < 3π/2
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\n" ); document.write( "reference angle a is in quadrant III where sin<0, cos<0
\n" ); document.write( "hypotenuse of reference right triangle in quadrant III=√(2^2+1^2)=√5
\n" ); document.write( "sina=2/√5=(2√5)/5
\n" ); document.write( "cosa=1/√5=√5/5
\n" ); document.write( "..
\n" ); document.write( "sin 2a=2sinacosa=2*(2√5)/5*√5/5=20/25=4/5
\n" ); document.write( "cos2a=cos^2a-sin^2a=5/25-20/25=-15/25=-3/5
\n" ); document.write( "tan2a=sin2a/cos2a=-4/3
\n" ); document.write( "..
\n" ); document.write( "Check: w/calculator
\n" ); document.write( "tan a=2 (Q3)
\n" ); document.write( "a=243.4349˚
\n" ); document.write( "2a=486.87˚
\n" ); document.write( "..
\n" ); document.write( "sin2a≈sin(486.87)≈0.7999...
\n" ); document.write( "exact value as computed=4/5=0.8
\n" ); document.write( "..
\n" ); document.write( "cos2a≈cos(486.87)≈-0.6000...
\n" ); document.write( "exact value as computed=-3/5=-0.6
\n" ); document.write( "..
\n" ); document.write( "tan2a≈tan(486.87)≈-1.3333...
\n" ); document.write( "exact value as computed=-4/3=-1.3333... \n" ); document.write( "
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