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Inverse Trigonometric Functions

Question

What is the principal value of $\cos^{- 1} (- \frac{\sqrt{3}}{2})$ ?

Solution

$Let \cos^{- 1} (- \frac{\sqrt{3}}{2}) = x \Rightarrow \cos x = - \frac{\sqrt{3}}{2} \Rightarrow \cos x = - \cos (\frac{π}{6}) \Rightarrow \cos x = \cos (π - \frac{π}{6}) \Rightarrow \cos x = \cos (\frac{5 π}{6}) \Rightarrow x = \frac{5 π}{6}$

Therefore, the principal value of $\cos^{- 1} (- \frac{\sqrt{3}}{2}) is \frac{5 π}{2}$

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Inverse Trigonometric Functions

What is the principal value of $\cos^{- 1} (- \frac{\sqrt{3}}{2})$ ?

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What is the principal value of $\cos^{- 1} (- \frac{\sqrt{3}}{2})$ ?