document.write( "Question 972617: Find the exact value of sin(2x) and cos(2x) if cosx= -1/3 and pi/2\n" ); document.write( "
Algebra.Com's Answer #595147 by lwsshak3(11628)\"\" \"About 
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Find the exact value of sin(2x) and cos(2x) if cosx= -1/3 and pi/2\n" ); document.write( "***
\n" ); document.write( "cosx=-1/3 (Q2)
\n" ); document.write( "sinx=√(1-cos^2(x))=√(1-1/9)=√(8/9)=√8/3
\n" ); document.write( "sin(2x)=2sinxcosx=2*√8/3*-1/3=-(2√8)/9
\n" ); document.write( "cos(2x)=cos^2(x)-sin^2(x)=1/9-8/9=-7/9
\n" ); document.write( "..
\n" ); document.write( "check:
\n" ); document.write( "cosx=-1/3(Q2)
\n" ); document.write( "x≈109.47˚
\n" ); document.write( "2x≈218.94˚
\n" ); document.write( "..
\n" ); document.write( "sin(2x)≈sin(218.94˚)≈-0.6285
\n" ); document.write( "exact value as computed=-(2√8)/9≈0.6285
\n" ); document.write( "..
\n" ); document.write( "cos(2x)≈cos(218.94˚)≈-0.7778
\n" ); document.write( "exact value as computed=-7/9≈-0.7778 \n" ); document.write( "
\n" );