SOLUTION: find the exact value of cos 2A and sin 2A given sin A = 12/13, A is in quadrant I

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Question 752005: find the exact value of cos 2A and sin 2A given sin A = 12/13, A is in quadrant I
Answer by lwsshak3(11628) About Me  (Show Source):
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find the exact value of cos 2A and sin 2A given sin A = 12/13, A is in quadrant I
sin%28A%29=12%2F13
cos%28A%29=5%2F13 ( working with 5-12-13 right triangle)
sin%282A%29=2sin%28A%29cos%28A%29=2%2A12%2F13%2A5%2F13=120%2F169
..
cos%282A%29=cos%5E2%28A%29-sin%5E2%28A%29=25%2F169-144%2F169=-119%2F169
..
Check with calculator:
sin(A)=12/13 (in Q1)
A=67.38º
2A=134.76
sin(2A)=sin(134.76º)≈0.71
exact value=120/169≈0.71
cos(2A)=cos(134.76º)≈-0.704
exact value=119/169≈-0.704