Question

Найти корень уравнения: sin t = - 1/2

Answer 1

$sin t = -\frac{1}{2}\\t=(-1)^{n+1}arcsin\frac{1}{2}+\pi n\\t=(-1)^{n+1}\frac{\pi}{6}+\pi n, \; n\in Z;\\\\1)\;t=-\frac{\pi}{6}+2\pi n, \; n\in Z;\\\\2)\; t=\pi -(- \frac{\pi}{6})+2\pi n\\t=\frac{7\pi}{6}+2\pi n, \; n\in Z.$