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INVERSE TRIGNOMETRIC FUNCTIONS — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSINVERSE TRIGNOMETRIC FUNCTIONS1 Mark
Question
Evaluate the following:
$\sin^{-1}(\sin4)$
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Answer

We know $\sin\big(\sin^{-1}\theta\big)=\theta$ if $-\frac{\pi}{2}\leq\theta\leq\frac{\pi}{2}$We have
$=\sin^{-1}(\sin4)$ $=\pi-4$ $\Big(\because\ \sin^{-1}(\sin\theta)=\pi-\theta,\text{if}\ \theta\in\Big[\frac{\pi}{2},\frac{3\pi}{2}\Big]\Big)$

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