Question

Определите знак числа: 1. Sin160 гр 2. cos200 гр 3.tg 310 гр 4.ctg (-400) гр 5.sin(-7Пи/11)гр 6.cos 31пи/5

Answer 1

$\displaystyle sin160`=sin(180-20)`=sin20`>0\\\\cos200`=cos(180+20)`=-cos20`<0\\\\tg310`=tg(360-50)`=-tg50`<0\\\\ctg(-400)=-ctg400=-ctg(360+40)=-ctg40<0\\\\sin(-7\pi/11)=-sin(7\pi/11)=-sin( \pi -3\pi /11)=-sin(3\pi/11)<0\\\\cos(31 \pi/5)=cos(6 \pi +\pi/5)=cos(\pi/5)>0$