============== 1 ==============
![arccos(-1)-arccos \frac{1}{2} -3 arccos(- \frac{ \sqrt{3} }{2} )= \\ = \pi -arccos1-arccos \frac{1}{2}-3( \pi -arccos \frac{ \sqrt{3} }{2}) = \pi -0- \frac{ \pi }{3} -3( \pi - \frac{ \pi }{6})=\\ = \frac{2 \pi }{3}- \frac{5 \pi }{2} =\frac{4 \pi }{6}- \frac{15 \pi }{6} =- \frac{ 11\pi }{6}](https://tex.z-dn.net/?f=arccos%28-1%29-arccos+%5Cfrac%7B1%7D%7B2%7D+-3+arccos%28-+%5Cfrac%7B+%5Csqrt%7B3%7D+%7D%7B2%7D+%29%3D+%5C%5C+%3D+%5Cpi+-arccos1-arccos+%5Cfrac%7B1%7D%7B2%7D-3%28+%5Cpi+-arccos+%5Cfrac%7B+%5Csqrt%7B3%7D+%7D%7B2%7D%29+%3D+%5Cpi+-0-+%5Cfrac%7B+%5Cpi+%7D%7B3%7D+-3%28+%5Cpi+-+%5Cfrac%7B+%5Cpi+%7D%7B6%7D%29%3D%5C%5C+%3D+%5Cfrac%7B2+%5Cpi+%7D%7B3%7D-+%5Cfrac%7B5+%5Cpi+%7D%7B2%7D+%3D%5Cfrac%7B4+%5Cpi+%7D%7B6%7D-+%5Cfrac%7B15+%5Cpi+%7D%7B6%7D+%3D-+%5Cfrac%7B+11%5Cpi+%7D%7B6%7D+)
============== 2 ==============
![2cos t=1\\ cost= \frac{1}{2} \\ t=\pm arccos\frac{1}{2}+2 \pi k, k \in Z\\ t=\pm \frac{ \pi }{3}+2 \pi k, k \in Z\\](https://tex.z-dn.net/?f=2cos+t%3D1%5C%5C%0Acost%3D+%5Cfrac%7B1%7D%7B2%7D+%5C%5C%0At%3D%5Cpm+arccos%5Cfrac%7B1%7D%7B2%7D%2B2+%5Cpi+k%2C+k+%5Cin+Z%5C%5C%0At%3D%5Cpm+%5Cfrac%7B+%5Cpi+%7D%7B3%7D%2B2+%5Cpi+k%2C+k+%5Cin+Z%5C%5C)
============== 3 ==============
![-2cos t=0 |:(-2)\\ cost=0\\ t= \frac{ \pi }{2} + \pi k, k \in Z](https://tex.z-dn.net/?f=-2cos+t%3D0+%7C%3A%28-2%29%5C%5C%0Acost%3D0%5C%5C%0At%3D+%5Cfrac%7B+%5Cpi+%7D%7B2%7D+%2B+%5Cpi+k%2C+k+%5Cin+Z)
============== 4 ==============
![cos (arcctg \sqrt{3} )=cos \frac{ \pi }{6} = \frac{ \sqrt{3} }{2}](https://tex.z-dn.net/?f=cos+%28arcctg++%5Csqrt%7B3%7D+%29%3Dcos+%5Cfrac%7B+%5Cpi+%7D%7B6%7D+%3D+%5Cfrac%7B+%5Csqrt%7B3%7D+%7D%7B2%7D+)
============== 5 ==============
![arcctg (ctg \frac{2 \pi }{3} )= \frac{2 \pi }{3}](https://tex.z-dn.net/?f=arcctg+%28ctg++%5Cfrac%7B2+%5Cpi+%7D%7B3%7D+%29%3D+%5Cfrac%7B2+%5Cpi+%7D%7B3%7D)
============== 6 ==============
![ctg x=-0,5\\ x=arcctg(-0.5)+ \pi n, n \in Z\\ x= \pi -arcctg(0.5)+ \pi n, n \in Z\\](https://tex.z-dn.net/?f=ctg+x%3D-0%2C5%5C%5C+x%3Darcctg%28-0.5%29%2B+%5Cpi+n%2C+n+%5Cin+Z%5C%5C+x%3D+%5Cpi+-arcctg%280.5%29%2B+%5Cpi+n%2C+n+%5Cin+Z%5C%5C)
============== 7 ==============
![ctg x=0\\ x=arcctg0+ \pi n, n \in Z\\ x= \frac{ \pi }{2} + \pi n, n \in Z\\](https://tex.z-dn.net/?f=ctg+x%3D0%5C%5C%0Ax%3Darcctg0%2B+%5Cpi+n%2C+n+%5Cin+Z%5C%5C+x%3D++%5Cfrac%7B+%5Cpi+%7D%7B2%7D+%2B+%5Cpi+n%2C+n+%5Cin+Z%5C%5C)
Y=kx+b
A(5;0);B(-2;21)
{0=5k+b;
{21=-2k+b
{b=-5k
{21=-2k-5k;7k=-21;k=-3
b=-5k=15
уравнение прямой
y=-3х+15
Проанализируем основание
√3/2 ≈ 0,86
Так как 0 < 0,86 < 1, то данная функция является убывающей