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

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Question 923012: Angle x is between (pi,3pi/2) and cos squared x = 10/11. Determine the exact value of sin2x and cotx
This is from my grade 12 advanced functions trig unit!!
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Angle x is between (pi,3pi/2) and cos squared x = 10/11. Determine the exact value of sin2x and cotx
cos%5E2%28x%29=10%2F11 (pi,3pi/2)
sin^2(x)=1-cos^2(x)=1-10/11=1/11
sinx=-√(1/11)(In quadrant III where sin<0)
cosx=-√(10/11)(In quadrant III where cos<0)
sin(2x)=2sinx*cosx=2*-√(1/11)*-√(10/11)=2√10/11
cotx=cosx/sinx=√((10/11)/(1/11))=√10
..
Check:
sinx=√(1/11)
x≈197.55˚
2x≈395.10˚
sin(2x)≈sin(395.10)≈0.575 (w/calculator)
Exact value as computed=2√10/11≈0.575
..
cotx≈cot(197.55)≈3.162(w/calculator)
Exact value as computed=√10≈3.162