document.write( "Question 921495: Given that cosx= -12/37 and x is in Quadrant 3, determine sin2x, cos2x, and tan2x. Which quadrant is 2x in? \n" ); document.write( "

Algebra.Com's Answer #559028 by lwsshak3(11628) $\"\"$ $\"About$

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Given that cosx= -12/37 and x is in Quadrant 3, determine sin2x, cos2x, and tan2x. Which quadrant is 2x in?
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\n" ); document.write( "cosx=-12/37
\n" ); document.write( "x≈251.08˚
\n" ); document.write( "2x≈142.15˚
\n" ); document.write( "sinx=-√(1-cos^2x)=-√(1-144/1369)=-√(1225/1369)=-35/37
\n" ); document.write( "..
\n" ); document.write( "sin2x=2sinxcosx=2*-35/37*-12/37=840/1369
\n" ); document.write( "cos2x=cos^2x-sin^2x=(-12/37)^2-(-35/37)^2=144/1369-1225/1369=-1081/1369
\n" ); document.write( "tan2x=sin/cos=840/-1081=-840/1081
\n" ); document.write( "..
\n" ); document.write( "calculator check:
\n" ); document.write( "sin2x=sin(142.15)≈0.6136
\n" ); document.write( "exact value=840/1369≈0.6136
\n" ); document.write( "..
\n" ); document.write( "cos2x=cos(142.15)≈-0.7896
\n" ); document.write( "exact value=-1081/1369≈-0.7896
\n" ); document.write( "..
\n" ); document.write( "tan2x=tan(142.15)≈-0.7770
\n" ); document.write( "exact value=-840/1081≈-0.7770 \n" ); document.write( "

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