Let be the sine function .

MATHEMATICS · Multi-part · CBSE · Mathematics · Inverse Trigonometric Functions · Inverse Trigonometric Functions

Problem

Let s:R→[−1,1]s: \mathbb R \to [-1,1] be the sine function s(x)=sin⁡xs(x)=\sin x. (i) Determine all intervals of the form (α,β)(\alpha, \beta) on which ss is injective. (ii) Show that no interval with length greater than π\pi can serve as a domain on which ss is injective. (iii) Write any two distinct maximal intervals on which ss is injective and state the corresponding inverse functions.

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