Question

найдите значения выражений

Answer 1

$2)\frac{2Cos(-2\pi-\beta)+Sin(-\frac{\pi }{2}+\beta)}{2Cos(\beta+\pi)}=\frac{2Cos(2\pi+\beta)-Sin(\frac{\pi}{2}-\beta)}{2Cos(\pi+\beta)}=\frac{2Cos\beta-Cos\beta}{-2Cos\beta}=-\frac{Cos\beta}{2Cos\beta}=-\frac{1}{2}=-0,5$

$3)-15Cos(\frac{7\pi }{2}-\alpha)=-15Cos[4\pi-(\frac{\pi }{2}+\alpha)]=-15Cos(\frac{\pi }{2}+\alpha )=-15*(-Sin\alpha)=15Sin\alpha\\\\1,5\pi<\alpha<2\pi \Rightarrow Sin\alpha<0\\\\Sin\alpha=-\sqrt{1-Cos^{2}\alpha}=-\sqrt{1-(\frac{7}{25})^{2}}=-\sqrt{1-\frac{49}{625} }=-\sqrt{\frac{576}{625}}=-\frac{24}{25}\\\\15Sin\alpha=15*(-\frac{24}{25} )=- 14,4$

$4)tg(\alpha-\frac{\pi }{2})=-tg(\frac{\pi }{2}-\alpha)=-Ctg\alpha\\\\-Ctg\alpha=-\frac{1}{tg\alpha}=-\frac{1}{0,04}=-25$