Question

Значение тригонометрических функций , вычислите значения выражения

Answer 1

Ответ:

11.cos(3,5p)=cos270°= 0

12.tg(5p/4)tg225°=tg(270°-45°)=ctg45°=1

13.cos(5p/3)=cos300°=cos(270°+30°)=sin30°=1/2

14.sin(10p/3)=sin600°=sin240°=sin(270°-30°)=-cos30°=-√3/2

15. cos(-960)=cos240°=cos(270-30)=-sin30=-1/2

16.tg750°=tg30°=√3/3

17.ctg1110°= ctg30°=√3

18.sin(-13p/3)=-sin60°=-√3/2

19.ctg(-13p/6)=ctg390°=-ctg30°=-√3

20.cos(-29p/4)=cos1305°=cos225°=cos(270°-45°)=-sin45°=-√2/2

Answer 2

$\displaystyle cos3.5\pi =cos(2\pi +\pi +\frac{\pi }{2})=cos(\frac{3\pi }{2})=0\\\\tg\frac{5\pi }{4}=tg(\pi+\frac{\pi }{4})=tg\frac{\pi }{4}=1\\\\cos(\frac{5\pi }{3})=cos(\pi+\frac{2\pi }{3})=-cos(\frac{2\pi }{3})= -(-\frac{1}{2})=\frac{1}{2}\\\\sin(\frac{10\pi }{3})=sin(2\pi+\pi +\frac{\pi }{3})=sin(\pi +\frac{\pi }{3})=-sin(\frac{\pi }{3})=-\frac{\sqrt{3}}{2}\\\\cos(-960`)=cos(-(4\pi +\pi +60`))=cos(\pi +60`)=-cos60`= -\frac{1}{2}\\\\tg750`=tg( 4\pi +30`)=tg30`=\frac{1}{\sqrt{3}}$

$\displaystyle ctg(1110`)=ctg(6\pi +30`)=ctg30=\sqrt{3}\\\\sin(-\frac{13}{3}\pi)=sin(-(4\pi +\frac{\pi}{3})=-sin\frac{\pi}{3}=-\frac{\sqrt{3}}{2}\\\\ctg(-\frac{13\pi}{6})=-ctg(2\pi+\frac{\pi }{6})=-ctg\frac{\pi }{6}=-\sqrt{3}\\\\cos(-\frac{29}{4}\pi)=cos(6\pi +\pi +\frac{\pi }{4})=-cos\frac{\pi }{4}=-\frac{\sqrt{2}}{2}$