Question

Выразите число через синус или косинус положительного угла,не превышающего П/4
1)Sin П/3
2)Cos П/3
3)Sin 5П/7
4)Cos 11П/13
5)Sin 13П/5
6)Cos 14П/5
7)Cos 29П/7
8)Sin 24П/7

Answer 1

1) $sin(\pi/3)=cos(\pi/2-\pi/3)=cos(\pi/6)\\ 2) cos(\pi/3)=sin(\pi/2-\pi/3)=sin(\pi/6)\\ 3) sin(5\pi/7)=cos(\pi/2-5\pi/7)=cos(-3\pi/14)=cos(3\pi/14)\\ 4) cos(11\pi/13)=-cos(\pi-11\pi/13)=-cos(2\pi/13)\\ 5)sin(13\pi/5)=sin(2\pi+3\pi/5)=cos(\pi/2-3\pi/5)=cos(-\pi/10)=\\=cos(\pi/10)\\ 6)cos(14\pi/5)=cos(2\pi+4\pi/5)=-cos(\pi-4\pi/5)=-cos(\pi/5)\\ 7) cos(29\pi/7)=cos(2\pi+2\pi+\pi/7)=cos(\pi/7)\\ 8)sin(24\pi/7)=sin(2\pi+2\pi-4\pi/7)=sin(-4\pi/7)=-sin(4\pi/7)=\\=-cos(\pi/2-4\pi/7)=-cos(-\pi/14)=-cos(\pi/14)$