SOLUTION: Use identities to find values of the sine and cosine functions for each angle measure. 2(theta), given sin(theta)=2/5 and cos(theta)<0

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Question 915968: Use identities to find values of the sine and cosine functions for each angle measure. 2(theta), given sin(theta)=2/5 and cos(theta)<0
Answer by lwsshak3(11628) About Me  (Show Source):
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Use identities to find values of the sine and cosine functions for each angle measure. 2(theta), given sin(theta)=2/5 and cos(theta)<0
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use x for theta
sin(x)=2/5 (in quadrant II, where sin>0,cos<0)
cos(x)=√(1-sin^2(x))=√1-4/25)=√(21/25)=√21/5
For measured angle 2x:
sin(2x)=2sin(x)cos(x)=2*2/5*√21/5=4√21/25
cos(2x)=cos^2(x)-sin^2(x)=21/25-4/25=17/25