Question 876535
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(15^2+8^2)=sqrt(225+64)=sqrt(289)=17}}}
{{{sin(theta)=15/17}}}
{{{cos(theta)=8/17}}}
{{{cos(2theta)=cos^2(theta)-sin^2(theta)=64/289-225/289=-161/289}}}
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