kuvitia9f

2021-12-26

What is ${\mathrm{cos}}^{-1}\left(\frac{1}{2}\right)$ ?

Lindsey Gamble

Explanation:
$\mathrm{arccos}x=\frac{1}{2}$
Trig table of special arcs gives
$\mathrm{cos}x=\frac{1}{2}\to x=\frac{\pi }{3}$
Trig unit circle gives another arc x that has the same $\mathrm{cos}$ value
$\mathrm{cos}x=\frac{12}{\to }x=-\frac{\pi }{3}$, or $x=\frac{5\pi }{3}$ (co-terminal)
Answers: $\frac{\pi }{3}$ and $\frac{5\pi }{3}$

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