Question

Решите :

1) 25sin(x)/3=-25/3

2) 11сos(x)/3=-11*2√2 /3

Answer 1

$1)\; \; 25\, sin\frac{x}{3}=-\frac{25}{3}\\\\sin\frac{x}{3}=-\frac{1}{3}\\\\\frac{x}{3}=(-1)^{n}\cdot arcsin(-\frac{1}{3})+\pi n\; ,\; n\in Z\\\\\frac{x}{3}=(-1)^{n+1}\cdot arcsin\frac{1}{3}+\pi n\; ,\; n\in Z\\\\x=(-1)^{n+1}\cdot 3\, arcsin\frac{1}{3}+3\pi n\; ,\; n\in Z$

$2)\; \; 11\, cos\frac{x}{3}=-11\cdot \frac{2\sqrt2}{3}\; \; ,\\\\cos\frac{x}{3}=-\frac{2\sqrt2}{3}\; \; ,\; \; -\frac{2\sqrt2}{3}\approx -0,94\; \; ,\; \; -1\leq -0,94\leq 1\; \; \Rightarrow \\\\\frac{x}{3}=\pm arccos(-\frac{2\sqrt2}{3})+2\pi n\; ,\; n\in Z\\\\\frac{x}{3}=\pm (\pi -arccos\frac{2\sqrt2}{3})+2\pi n\; ,\; n\in Z\\\\x=\pm 3(\pi -arccos\frac{2\sqrt2}{3})+6\pi n\; ,\; n\in Z$