SOLUTION: Find the exact value of sin(2x) and cos(2x) if cosx= -1/3 and pi/2<x<pi

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Question 972617: Find the exact value of sin(2x) and cos(2x) if cosx= -1/3 and pi/2
Answer by lwsshak3(11628) About Me  (Show Source):
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Find the exact value of sin(2x) and cos(2x) if cosx= -1/3 and pi/2 ***
cosx=-1/3 (Q2)
sinx=√(1-cos^2(x))=√(1-1/9)=√(8/9)=√8/3
sin(2x)=2sinxcosx=2*√8/3*-1/3=-(2√8)/9
cos(2x)=cos^2(x)-sin^2(x)=1/9-8/9=-7/9
..
check:
cosx=-1/3(Q2)
x≈109.47˚
2x≈218.94˚
..
sin(2x)≈sin(218.94˚)≈-0.6285
exact value as computed=-(2√8)/9≈0.6285
..
cos(2x)≈cos(218.94˚)≈-0.7778
exact value as computed=-7/9≈-0.7778