If $cos θ = - \frac{15}{17}$ $costheta=-15/17$ and $\frac{π}{2} < θ < π$ $pi/2<theta<pi$ , how do you find $cos 2 θ$ $cos2theta$ ?

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If $cos θ = - \frac{15}{17}$ $costheta=-15/17$ and $\frac{π}{2} < θ < π$ $pi/2<theta<pi$ , how do you find $cos 2 θ$ $cos2theta$ ?

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Answer 1 · 2016-11-12T12:45:47

$\frac{161}{289}$ $161/289$

Explanation:

Since $cos 2 θ = {cos}^{2} θ - {sin}^{2} θ$ $cos2theta=cos^2theta-sin^2theta$

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

$cos 2 θ = {cos}^{2} θ - (1 - {cos}^{2} θ) = 2 {cos}^{2} θ - 1$ $cos2theta=cos^2theta-(1-cos^2theta)=2cos^2theta-1$
$= 2 {(- \frac{15}{17})}^{2} - 1$ $=2(-15/17)^2-1$
$= 2 \cdot \frac{225}{289} - 1$ $=2*225/289-1$
$= \frac{450 - 289}{289} = \frac{161}{289}$ $=(450-289)/289=161/289$

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If $cos θ = - \frac{15}{17}$ $costheta=-15/17$ and $\frac{π}{2} < θ < π$ $pi/2<theta<pi$ , how do you find $cos 2 θ$ $cos2theta$ ?

1 Answer

Explanation:

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If cosθ=−1517costheta=-15/17 and π2<θ<πpi/2<theta<pi, how do you find cos2θcos2theta?

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Explanation:

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If $cos θ = - \frac{15}{17}$ $costheta=-15/17$ and $\frac{π}{2} < θ < π$ $pi/2<theta<pi$ , how do you find $cos 2 θ$ $cos2theta$ ?