document.write( "Question 924316: Find sin 2x, cos 2x, and tan 2x from the given information.
\n" ); document.write( "csc x = 6, tan x < 0
\n" ); document.write( "sin 2x =
\n" ); document.write( "cos 2x =
\n" ); document.write( "tan 2x = \r
\n" ); document.write( "\n" ); document.write( "please help
\n" ); document.write( "Thank you \n" ); document.write( "
Algebra.Com's Answer #560780 by lwsshak3(11628)\"\" \"About 
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Find sin 2x, cos 2x, and tan 2x from the given information.
\n" ); document.write( "csc x = 6, tan x < 0
\n" ); document.write( "***
\n" ); document.write( "Reference angle x is in quadrant II where sin>0, cos<0
\n" ); document.write( "sinx=1/cscx=1/6
\n" ); document.write( "cosx=-√(1-sin^2(x))=-√(1-1/36)=-√(35/36)=-√35/6
\n" ); document.write( "..
\n" ); document.write( "sin(2x)=2sinxcosx=2*1/6*-√35/6=-2√35/36
\n" ); document.write( "cos(2x)=cos^2(x)-sin^2(x)=35/36-1/36=34/36
\n" ); document.write( "tan(2x)=sin(2x)/cos(2x)=-2√35/34
\n" ); document.write( "..
\n" ); document.write( "check:
\n" ); document.write( "sinx=1/6
\n" ); document.write( "x≈170.41
\n" ); document.write( "2x≈340.81
\n" ); document.write( "sin(2x)≈sin(340.81˚)=-0.3287
\n" ); document.write( "exact value as computed=-2√35/36≈-0.3287
\n" ); document.write( "..
\n" ); document.write( "cos(2x)=cos(340.81)≈0.9444
\n" ); document.write( "exact value as computed=34/36≈0.9444
\n" ); document.write( "..
\n" ); document.write( "tan(2x)=tan(340.81)≈-0.3480
\n" ); document.write( "exact value as computed=-2√35/34≈-0.3480 \n" ); document.write( "
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