document.write( "Question 820569: Find the exact values of sin2u, cos2u, and tan2u. cotu=-6, 3pi/2\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #493714 by lwsshak3(11628)\"\" \"About 
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Find the exact values of sin2u, cos2u, and tan2u. cotu=-6, 3pi/2
\n" ); document.write( "assume given interval: [0,3π/2]
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\n" ); document.write( "reference angle in quadrant II where sin>0, cos<0, cot<0, tan<0
\n" ); document.write( "cotu=-6=1/tanu
\n" ); document.write( "tanu=-1/6
\n" ); document.write( "hypotenuse of reference right triangle=√(1^2+6^2)=√(1+36)=√37
\n" ); document.write( "..
\n" ); document.write( "sinu=1/√37=√37/37
\n" ); document.write( "cosu=-6/√37=-6√37/37
\n" ); document.write( "tanu=-1/6
\n" ); document.write( "..
\n" ); document.write( "sin2u=2sinucosu=2*√37/37*-6√37/37=-444/1369
\n" ); document.write( "cos2u=cos^2u-sin^2u=36/37-1/37=35/37
\n" ); document.write( "tan2u=(2tanu)/(1-tan^2u)=-2/6/(1-1/36)=(-12/36)/35/36=-12/35
\n" ); document.write( "..
\n" ); document.write( "calculator check:
\n" ); document.write( "tanu=-1/6
\n" ); document.write( "u≈170.5376˚
\n" ); document.write( "2u≈341.0754˚(In quadrant IV where sin<0, cos>0, tan<0)
\n" ); document.write( "..
\n" ); document.write( "sin2u=sin(341.0754)≈-0.3243..
\n" ); document.write( "exact value as calculated=-444/1369≈-0.3243..
\n" ); document.write( "..
\n" ); document.write( "cos2u=cos(341.0754)≈0.9459..
\n" ); document.write( "exact value as calculated=35/37≈0.9459..
\n" ); document.write( "..
\n" ); document.write( "tan2u=tan(341.0754)≈-0.3428..
\n" ); document.write( "exact value as calculated=-12/35≈-0.3428..\r
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