Question

Решите уравнение:arcsin5x=п/3

Answer 1

Ответ:

$arc \sin5x = \frac{\pi}{3}$

$5x < - 1 \\ 5x > 1$

$x < - \frac{1}{5} \\ x > \frac{1}{5}$

$x∈ < - \infty . - \frac{1}{5} > U < \frac{1}{5} . + \infty >$

$arc \sin5x = \frac{\pi}{3} .x∈[ - \frac{1}{5}. \frac{1}{5} ]$

$5x = \sin \frac{\pi}{3}$

$5x = \frac{ \sqrt{3} }{2}$

$5x \div 5 = \frac{ \sqrt{3} }{2} \div 5$

$x = \frac{ \sqrt{3} }{2} \times \frac{1}{5}$

$x = \frac{ \sqrt{3} }{10} .x∈[ - \frac{1}{5} . \frac{1}{5} ]$

$x = \frac{ \sqrt{3} }{10}$