Question

Обчисліть
1) arccos(-1) + 2arccos 1/2
2)arccos1-п
3)arcsin(-1/2) - arccos √3/2
4) arcsin 1/2 + arccos (-√3/2)
5) arcsin1 + arccos(-1)
6) arccos (-√2/2) - arccos √2/2

Answer 1

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

$4)arcSin\frac{1}{2}+arcCos(-\frac{\sqrt{3} }{2})=\frac{\pi }{6}+\frac{5\pi }{6}=\frac{6\pi }{6}=\pi\\\\5)arcSin1+arcCos(-1)=\frac{\pi }{2}+\pi=\frac{3\pi }{2}\\\\6)arcCos(-\frac{\sqrt{2} }{2})-arcCos\frac{\sqrt{2} }{2}=\frac{3\pi }{4}-\frac{\pi }{4}=\frac{2\pi }{4}=\frac{\pi }{2}$