Question

При каких значениях x неравенство sinxcosx<=1/4 будет верным?

Answer 1

$Sinx Cosx\leq\dfrac{1}{4} \\\\2\cdot Sinx Cosx\leq2\cdot \dfrac{1}{4}\\\\Sin2x\leq \dfrac{1}{2}\\\\-\pi-arcSin\dfrac{1}{2}+2\pi k\leq2x\leq arcSin\dfrac{1}{2}+2\pi k,k\in Z\\\\-\pi -\dfrac{\pi }{6}+2\pi k \leq 2x\leq \dfrac{\pi }{6}+2\pi k,k\in Z\\\\-\dfrac{7\pi }{6}+2\pi k \leq2x\leq \dfrac{\pi }{6}+2\pi k,k\in Z\\\\-\dfrac{7\pi }{12} +\pi k\leq x \leq \dfrac{\pi }{12}+\pi k,k\in Z\\\\Otvet:\boxed{x\in\Big[-\dfrac{7\pi }{12} +\pi k \ ; \ \dfrac{\pi }{12}+\pi k\Big]}$