Let f(x)={−2sin⁡x,for −π≤x≤−π2asin⁡x+b,for −π2<x<π2cos⁡x,for π2≤x≤πf(x) = \begin{cases} -2\sin x, & \text{for } -\pi \le x \le -\frac{\pi}{2} \\ a \sin x + b, & \text{for } -\frac{\pi}{2} < x < \frac{\pi}{2} \\ \cos x, & \text{for } \frac{\pi}{2} \le x \le \pi \end{cases}…

Mathematics

Problem

Let f(x)={−2sin⁡x,for −π≤x≤−π2asin⁡x+b,for −π2<x<π2cos⁡x,for π2≤x≤πf(x) = \begin{cases} -2\sin x, & \text{for } -\pi \le x \le -\frac{\pi}{2} \\ a \sin x + b, & \text{for } -\frac{\pi}{2} < x < \frac{\pi}{2} \\ \cos x, & \text{for } \frac{\pi}{2} \le x \le \pi \end{cases} . If ff is continuous on [−π,π][-\pi, \pi] , then find the values of aa and bb .

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