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Inverse Trigonometric Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions1 Mark
MCQ
Find the principal values of: $\cos ^{-1}\left(\frac{1}{2}\right)$
  • A
    $-\frac{\pi}{3}$
  • ✓
    $\frac{\pi}{3}$
  • C
    $\frac{\pi}{2}$
  • D
    $\frac{2 \pi}{3}$
✓

Answer

Correct option: B.
$\frac{\pi}{3}$
(b) : Let $\cos ^{-1}\left(\frac{1}{2}\right)=\theta \Rightarrow \cos \theta=\frac{1}{2}=\cos \frac{\pi}{3}$
$\Rightarrow \theta=\frac{\pi}{3} \in[0, \pi]$
$\therefore$ Principal value of $\cos ^{-1}\left(\frac{1}{2}\right)$ is $\frac{\pi}{3}$.

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