Let be a real parameter

MATHEMATICS · Single correct · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions

Problem

Let kk be a real parameter. The inequality arcsin⁡(kx)≤π4\arcsin(kx) \le \dfrac{\pi}{4} must hold for every x∈[−1,1]x \in [-1,1]. Which of the following describes all possible values of kk? (a) ∣k∣≤1|k| \le 1 (b) 0≤k≤220 \le k \le \dfrac{\sqrt{2}}{2} (c) ∣k∣≤22|k| \le \dfrac{\sqrt{2}}{2} (d) ∣k∣≤π4|k| \le \dfrac{\pi}{4}

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