The function is not invertible on

MATHEMATICS · Single correct · A Level · Mathematics · Trigonometry · Trigonometry

Problem

The function s(x)=sin⁡xs(x)=\sin x is not invertible on R\mathbb R. Which of the following intervals, symmetric about the origin and contained in [−π,π][-\pi,\pi], can be taken as the domain of ss so that the function becomes one–one? (a) [0,π][0,\pi] (b) [−3π4,3π4]\left[-\dfrac{3\pi}{4},\dfrac{3\pi}{4}\right] (c) [−π2,π2]\left[-\dfrac{\pi}{2},\dfrac{\pi}{2}\right] (d) [0,π2]\left[0,\dfrac{\pi}{2}\right]

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