Question

Найдите значение выражения
3 arccos(-1/2)+4 arccos(-1/корень 2)+arccos 1
И
Arcsin(-1)+2arccos(-корень 3/2)-2arccos(-1)​

Answer 1

$1)3arcCos(-\frac{1}{2})+4arcCos(-\frac{1}{\sqrt{2}})+arcCos1= 3*\frac{2\pi}{3} +4*\frac{3\pi}{4} +0=2\pi+3\pi=5\pi\\\\\\2)arcSin(-1)+2arcCos(-\frac{\sqrt{3}}{2})-2arcCos(-1)=-\frac{\pi }{2}+2*\frac{5\pi }{6}-2*\pi=\\\\=-\frac{\pi }{2}+\frac{5\pi }{3} -2\pi= \frac{-3\pi+10\pi-12\pi}{6}=-\frac{5\pi }{6}$