Mathematics

Problem

Let

k

be a real parameter. The inequality

\arcsin(kx) \le \dfrac{\pi}{4}

must hold for every

x \in [-1,1]

. Which of the following describes all possible values of

k

? a)

|k| \le 1

0 \le k \le \dfrac{\sqrt{2}}{2}

|k| \le \dfrac{\sqrt{2}}{2}

|k| \le \dfrac{\pi}{4}