SOLUTION: Find the exact values of sin(2theta), and cos(2theta) if sin(theta)= -9/10 and theta is between 180 degrees and 270 degrees.

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Question 610303: Find the exact values of sin(2theta), and cos(2theta) if sin(theta)= -9/10 and theta is between 180 degrees and 270 degrees.
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find the exact values of sin(2theta), and cos(2theta) if sin(theta)= -9/10 and theta is between 180 degrees and 270 degrees.
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use x in place of theta.
sinx=-9/10=opposite side/hypotenuse (in quadrant III where sin is <0)
Adjacent side=√(10^2-9^2)=√(100-81)=√19
cosx=-√19/10 (in quadrant III where cos is also<0)
..
sin2x=2sinxcosx
=2*(-9/10)*(-√19/10)
=18√19/100
=(9√19)/50 (in quadrant II where sin>0)
..
cos2x=cos^2x-sin^2x
=(-√19/10)^2-(-9/10)^2
=19/100-81/100
=-62/100
=-31/50 (in quadrant II where cos<0)