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Question
Write the maximum and minimum values of sin (sin x).
Solution
We know:
\[ - 1 \leq \sin x \leq 1\]
\[\text { Also, }\sin\left( - \theta \right) = - \sin\theta\]
\[\text{ When the angle increases from 0 to }\frac{\pi}{2},\text{ the value of }\sin\theta\text{ also increases . }\]
\[ \therefore\text{ Maximum value of }\sin\left[ \sin\left( x \right) \right] = \sin\left( 1 \right)\]
\[\text{ And, minimum value of }\sin\left[ \sin\left( x \right) \right] = \sin\left( - 1 \right) = - \sin1\]
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