document.write( "Question 945485: Find the exact value of sine two theta given cosine of theta = 1 over 6 and theta is between 0 degrees and 90 degrees.. \n" ); document.write( "

Algebra.Com's Answer #576721 by lwsshak3(11628) $\"\"$ $\"About$

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Find the exact value of sine two theta given cosine of theta = 1 over 6 and theta is between 0 degrees and 90 degrees.
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\n" ); document.write( "cosx=1/6 (Q1)
\n" ); document.write( "sinx=√(1-cos^2(x))=√(1-(1/36))=√(35/36)=√35/6
\n" ); document.write( "sin2x=2sinxcosx=2*(1/6)(√35/6)=2√35/36
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\n" ); document.write( "check:
\n" ); document.write( "cosx=1/6
\n" ); document.write( "x≈80.4059
\n" ); document.write( "2x=160.81˚
\n" ); document.write( "sin(2x)=sin(160.81˚)≈0.3287
\n" ); document.write( "exact value as computed=2√35/36≈0.3287 \n" ); document.write( "

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