If $costheta=-15/17$ and $pi/2<theta<pi$ , how do you find $cos2theta$ ?

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Answer 1 · 2016-11-12T12:45:47

$161/289$

Since $cos2theta=cos^2theta-sin^2theta$

and $sin^2theta=1-cos^2theta$ , you will have:

$cos2theta=cos^2theta-(1-cos^2theta)=2cos^2theta-1$
$=2(-15/17)^2-1$
$=2*225/289-1$
$=(450-289)/289=161/289$

If costheta=-15/17costheta=-15/17 and pi/2<theta<pipi/2<theta<pi, how do you find cos2thetacos2theta?