How do you solve $cos x = \frac{1}{2}$ $cosx=1/2$ ?

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How do you solve $cos x = \frac{1}{2}$ $cosx=1/2$ ?

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Answer 1 · 2017-09-19T10:34:30

$x = \frac{π}{3} or x = \frac{5 π}{3}$ $x=pi/3" or "x=(5pi)/3$

Explanation:

$since cos x > 0$ $"since "cosx>0$

$then x will be in the first/fourth quadrants$ $"then x will be in the first/fourth quadrants"$

$cos x = \frac{1}{2}$ $cosx=1/2$

$\Rightarrow x = {cos}^{- 1} (\frac{1}{2}) = \frac{π}{3} \leftarrow angle in first quadrant$ $rArrx=cos^-1(1/2)=pi/3larrcolor(blue)" angle in first quadrant"$

$or x = (2 π - \frac{π}{3}) = \frac{5 π}{3} \leftarrow angle in fourth quadrant$ $"or "x=(2pi-pi/3)=(5pi)/3larrcolor(blue)" angle in fourth quadrant"$

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How do you solve $cos x = \frac{1}{2}$ $cosx=1/2$ ?

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How do you solve $cos x = \frac{1}{2}$ $cosx=1/2$ ?