Question

Решите пожалуйста мне завтра на пересдачу

Answer 1

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

$2)-3Sin(\frac{5\pi }{2}-\alpha)=-3Sin((2\pi+\frac{\pi }{2})-\alpha)=-3Sin(\frac{\pi }{2}-\alpha)=-3Cos\alpha\\\\\alpha\in(0,5\pi;\pi)\Rightarrow Cos\alpha<0\\\\Cos\alpha=-\sqrt{1-Sin^{2}\alpha}=-\sqrt{1-0,6^{2}}=-\sqrt{1-0,36}=-\sqrt{0,64}=-0,8\\\\-3Cos\alpha=-3*(-0,8)=2,4\\\\Otvet:\boxed{2,4}$

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