# How do you solve \cos^2 x = \frac{1}{16}  over the interval [0,2pi]?

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Nghi N Share
Apr 21, 2018

$x = \pm {75}^{\circ} 52$

#### Explanation:

${\cos}^{2} x = \frac{1}{16}$
$\cos x = \pm \frac{1}{4}$
Calculator and unit circle give -->
$x = \pm {75}^{\circ} 52$

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Apr 20, 2018

x=cos^(-1)(1/4)=1.32 ["rad"]=75.5°

#### Explanation:

${\cos}^{2} \left(x\right) = \frac{1}{16}$
$\cos \left(x\right) = \frac{1}{4}$
$x = {\cos}^{- 1} \left(\frac{1}{4}\right) = 1.32 \left[\text{rad}\right] = 75.5$

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