# How do you find the exact value of cos(theta) if sin(theta)=-2/3?

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#### Explanation

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I want someone to double check my answer

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polaris Share
Nov 8, 2015

$\cos \theta = \frac{\sqrt{5}}{3}$ (you didn't mention where your theta is)

#### Explanation:

$\sin \theta = \frac{y}{h}$
$\cos \theta = \frac{x}{h}$
but ${x}^{2} + {y}^{2} = {h}^{2}$
therefore ${x}^{2} = {h}^{2} - {y}^{2} = {3}^{2} - {\left(- 2\right)}^{2} = 9 - 4 = 5$
$x = \sqrt{5}$
thus, $\cos \theta = \frac{\sqrt{5}}{3}$
since your $\sin \theta$ is negative, theta could either be in Q III or Q IV
in Q III $\cos \theta = - \frac{\sqrt{5}}{3}$, in Q IV $\cos \theta = + \frac{\sqrt{5}}{3}$

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