# What is \cos^{-1}(\frac{1}{2}) ?

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

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