SOLUTION: Given that cos theta = -5/13 with theta in quadrant II, find tan 2 theta

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Question 876536: Given that cos theta = -5/13 with theta in quadrant II, find tan 2 theta
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Given that cos theta = -5/13 with theta in quadrant II, find tan 2 theta
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You are working with a (5-12-13) reference right triangle in quadrant II
cos%28theta%29=-5%2F13
sin%28theta%29=12%2F13
sin%282theta%29=2sin%28theta%29cos%28theta%29=2%2A12%2F13%2A-5%2F13=-120%2F169
cos%282theta%29=cos%5E2%28theta%29-sin%5E2%28theta%29=25%2F169-144%2F69=-119%2F69
tan%282theta%29=sin%282theta%29%2Fcos%282theta%29=120%2F119
Calculator check:
cos(theta)=-5/13
theta≈112.62
2theta≈225.24}}}
tan(2theta)≈tan(225.24)≈1.0084…
exact value as calculated=120/119≈1.0084…
let me know if my answer is correct and the procedure is understandable.