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Inverse Trigonometric Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions1 Mark
Question
Find the principal value of ${\cos ^{ - 1}}\left( { - \frac{1}{2}} \right)$.
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Answer

Let ${\cos ^{ - 1}}\left( { - \frac{1}{2}} \right) = \theta$
$\cos \theta = \frac{{ - 1}}{2}$
$\theta \in [0,\pi ]$
$\cos \theta = \cos \left( {\pi - \frac{\pi }{3}} \right)$
$\theta = \frac{{2\pi }}{3}$
Principal value is$\frac{{2\pi }}{3}$

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