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

kuvitia9f 2021-12-26 Answered
What is \(\displaystyle{{\cos}^{{-{1}}}{\left({\frac{{{1}}}{{{2}}}}\right)}}\) ?

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Expert Answer

Lindsey Gamble
Answered 2021-12-27 Author has 4878 answers
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 \(\displaystyle{\frac{{{5}\pi}}{{{3}}}}\)
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