反三角函數

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反三角函數值 \({\cos ^{ - 1}}\frac{1}{2} = ?\)

(A) \(\frac{\pi }{6}\) (B) \(\frac{\pi }{5}\) (C) \(\frac{\pi }{4}\) (D) \(\frac{\pi }{3}\)

詳解：\(\cos \frac{\pi }{6} = \frac{{\sqrt 3 }}{2}\quad \Rightarrow \quad {\cos ^{ - 1}}\frac{{\sqrt 3 }}{2} = \frac{\pi }{6}\)

\(\cos \frac{\pi }{4} = \frac{{\sqrt 2 }}{2}\quad \Rightarrow \quad {\cos ^{ - 1}}\frac{{\sqrt 2 }}{2} = \frac{\pi }{4}\)

\(\cos \frac{\pi }{3} = \frac{1}{2}\quad \Rightarrow \quad {\cos ^{ - 1}}\frac{1}{2} = \frac{\pi }{3}\)

故選(D)