For each integer

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

Problem

For each integer nn, consider the point (nπ,sin⁡nπ)(n\pi,\sin n\pi) on the curve y=sin⁡xy = \sin x. In the interval x∈[−2π, 3π]x \in [-2\pi,\,3\pi], for how many such integers nn does this point lie on a section of the curve where y=sin⁡xy = \sin x is increasing as xx increases? (a) 4 (b) 2 (c) 3 (d) 0

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