SOLUTION: If cos x = −4/5 and x is in quadrant II, find cos 2x and sin 2x.

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Question 825963: If cos x = −4/5 and x is in quadrant II, find cos 2x and sin 2x.
Answer by lwsshak3(11628) About Me  (Show Source):
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If cos x = −4/5 and x is in quadrant II, find cos 2x and sin 2x.
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cosx=-4/5(working with (3-4-5) reference right triangle in quadrant II in which cos<0, sin>0)
sinx=3/5
sin2x=2sinxcosx=2*3/5*(-4/5)=-24/5
cos2x=cos^2x-sin^2x=16/25-9/25=7/25
..
calculator check:
cosx=-4/5 (in quadrant II)
x≈142.13˚
2x≈286.26˚
..
cos2x≈cos(286.26)≈0.2799..
Exact value=7/25≈0.28
..
sin2x≈sin(286.26)≈-0.9600..
Exact value=-24/25≈-0.9600