SOLUTION: Given that tan theta = 15/8 with theta in quadrant I, find cos 2 theta

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Question 876535: Given that tan theta = 15/8 with theta in quadrant I, find cos 2 theta
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Given that tan theta = 15/8 with theta in quadrant I, find cos 2 theta
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Hypotenuse of working reference right triangle in quadrant I=sqrt%2815%5E2%2B8%5E2%29=sqrt%28225%2B64%29=sqrt%28289%29=17
sin%28theta%29=15%2F17
cos%28theta%29=8%2F17
cos%282theta%29=cos%5E2%28theta%29-sin%5E2%28theta%29=64%2F289-225%2F289=-161%2F289
calculator check:
tan theta=15/8
theta≈61.9275˚
2theta≈123.86˚
cos(2theta)≈cos(123.86˚)≈-0.5572…
Exact value=-161/189≈-0.5571…
let me know if my answer is correct and the method used is understandable