Question

Помогите!!! Найдите область значений функции
y=3/4π*arcsin(2−3x/5).

Answer 1

$-\frac{\pi}{2}\leq arcsin(2-\frac{3x}{5})\leq \frac{\pi}{2}\\\\-\frac{\pi}{2}\cdot \frac{3}{4\pi }\leq \frac{3}{4\pi }arcsin(2-\frac{3x}{5})\leq \frac{\pi}{2}\cdot \frac{3}{4\pi }\\\\-\frac{3}{8}\leq \frac{3}{4\pi }arcsin(2-\frac{3x}{5})\leq \frac{3}{8}$

$\frac{3}{4\pi }arcsin(2-\frac{3x}{5})\in [\, -\frac{3}{8}\, ;\, \frac{3}{8}\; ]$