Question

5sin^2t<=11sint+12
Решите срочно!!!

Answer 1

$5sin^2t \leq 11sint+12\\\\sint=p,\; \; -1 \leq sint \leq 1\; ,\; \; -1 \leq p \leq 1\\\\5p^2-11p-12 \leq 0\; ,\\\\p_{1,2}=\dfrac{11\pm \sqrt{361}}{10}=\dfrac{11\pm 19}{10}\ \ ,\ \ \ p_1=3\ \ \ ,\ \ p_2=-0,8\\\\5p^2-11p+12\leq 0\ \ \to \ \ -0,8\leq p\leq 3\\\\-0,8\leq sint\leq 1\\\\-arcsin0,8+2\pi n\leq t\leq \pi +arcsin0,8+2\pi n,\; n\in Z\\\\t\in (-arcsin0,8+2\pi n\ ;\ \pi +arcsin0,8+2\pi n)\ ,\; n\in Z$