Question 972617
Find the exact value of sin(2x) and cos(2x) if cosx= -1/3 and pi/2<x<pi
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cosx=-1/3 (Q2)
sinx=&#8730;(1-cos^2(x))=&#8730;(1-1/9)=&#8730;(8/9)=&#8730;8/3
sin(2x)=2sinxcosx=2*&#8730;8/3*-1/3=-(2&#8730;8)/9
cos(2x)=cos^2(x)-sin^2(x)=1/9-8/9=-7/9
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check:
cosx=-1/3(Q2)
x&#8776;109.47&#730;
2x&#8776;218.94&#730;
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sin(2x)&#8776;sin(218.94&#730;)&#8776;-0.6285
exact value as computed=-(2&#8730;8)/9&#8776;0.6285
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cos(2x)&#8776;cos(218.94&#730;)&#8776;-0.7778
exact value as computed=-7/9&#8776;-0.7778