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Find sin 2x, cos 2x, and tan 2x from the given information.
\n" ); document.write( "tan x = −1/6, cos x > 0
\n" ); document.write( "reference angle x is in quadrant IV where cos>0, sin<0
\n" ); document.write( "hypotenuse of reference right triangle in quadrant IV=√(6^2+1^2)=√(36+1)=√37
\n" ); document.write( "sinx=-1/√37=-√37/37
\n" ); document.write( "cosx=6/√37=(6√37)/37
\n" ); document.write( "..
\n" ); document.write( "sin(2x)=2sinxcosx=2*-√37/37*6√37/37=-444/1369
\n" ); document.write( "cos(2x)=cos^2(x)-sin^2(x)=36/37-1/37=35/37
\n" ); document.write( "tan(2x)=sin(2x)/cos(2x)=16428/47915
\n" ); document.write( "..
\n" ); document.write( "Check:
\n" ); document.write( "tanx=1/6(Q4)
\n" ); document.write( "x=350.538
\n" ); document.write( "2x=701.075
\n" ); document.write( "..
\n" ); document.write( "sin(2x)=sin(701.075)=-0.3243
\n" ); document.write( "exact value as computed=-444/1369≈-0.3243
\n" ); document.write( "..
\n" ); document.write( "cos(2x)=cos(701.075)=0.9459
\n" ); document.write( "exact value as computed=35/37≈0.9459 \n" ); document.write( "