You can put this solution on YOUR website! what is cos(2theta) if cos=1/3 and csc<0
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csc<0 in quadrants III and IV
cos>0 in quadrants I and IV
so, we are working with reference angle in quadrant IV
cosx=1/3=adjacent side/hypotenuse in quadrant IV where cos>0
opposite side=√(3^2-1^2)=√(9-1)=√8
sinx=opposite side/hypotenuse=-√8/3(in quadrant IV where sin<0
cos2x=cos^2x-sin^2x=1/9-8/9=-7/9
Check:
cos^-1=1/3
x≈70.529º
2x≈141.05756º
cos2x≈-0.7777..
-7/9≈-0.7777..
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