SOLUTION: Use identities(double-angle) to find the values of the sine and cosine functions for each angle measure. 2&#415; given that cos x = -5/13 and sin &#415;

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Question 922908: Use identities(double-angle) to find the values of the sine and cosine functions for each angle measure.
2Ɵ given that cos x = -5/13 and sin Ɵ > 0
Answer by lwsshak3(11628) (Show Source):
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Use identities(double-angle) to find the values of the sine and cosine functions for each angle measure.
2Ɵ given that cos x = -5/13 and sin Ɵ > 0
***
You are working with a (5-12-13) reference right triangle in quadrant II.
cosx=-5/13
sinx=12/13
sin(2x)=2sinxcosx=2*12/13*-5/13=-120/169
cos(2x)=cos^2(x)-sin^2(x)=25/169-144/169=-119/169
Check:
cosx=-5/13
x≈112.62˚
2x=225.24
..
sin(2x)≈sin(225.24)≈-0.7100 (w/calculator)
Exact value=-120/119≈-0.7100
..
cos(2x)≈cos(225.24)≈-0.7041 (w/calculator)
Exact value=-119/169≈-0.7041

SOLUTION: Use identities(double-angle) to find the values of the sine and cosine functions for each angle measure. 2&#415; given that cos x = -5/13 and sin &#415; > 0

SOLUTION: Use identities(double-angle) to find the values of the sine and cosine functions for each angle measure. 2Ɵ given that cos x = -5/13 and sin Ɵ > 0