document.write( "Question 923012: Angle x is between (pi,3pi/2) and cos squared x = 10/11. Determine the exact value of sin2x and cotx
\n" ); document.write( "This is from my grade 12 advanced functions trig unit!! \n" ); document.write( "

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Angle x is between (pi,3pi/2) and cos squared x = 10/11. Determine the exact value of sin2x and cotx
\n" ); document.write( " $\"cos%5E2%28x%29=10%2F11\"$ (pi,3pi/2)
\n" ); document.write( "sin^2(x)=1-cos^2(x)=1-10/11=1/11
\n" ); document.write( "sinx=-√(1/11)(In quadrant III where sin<0)
\n" ); document.write( "cosx=-√(10/11)(In quadrant III where cos<0)
\n" ); document.write( "sin(2x)=2sinx*cosx=2*-√(1/11)*-√(10/11)=2√10/11
\n" ); document.write( "cotx=cosx/sinx=√((10/11)/(1/11))=√10
\n" ); document.write( "..
\n" ); document.write( "Check:
\n" ); document.write( "sinx=√(1/11)
\n" ); document.write( "x≈197.55˚
\n" ); document.write( "2x≈395.10˚
\n" ); document.write( "sin(2x)≈sin(395.10)≈0.575 (w/calculator)
\n" ); document.write( "Exact value as computed=2√10/11≈0.575
\n" ); document.write( "..
\n" ); document.write( "cotx≈cot(197.55)≈3.162(w/calculator)
\n" ); document.write( "Exact value as computed=√10≈3.162
\n" ); document.write( " \n" ); document.write( "

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