Question

Тригонометрия, формулы привидения

Answer 1

$1)\frac{Cos(2\pi-\beta)+2Sin(-\frac{3\pi }{2}+\beta)}{2Cos(\beta+2\pi)}=\frac{Cos\beta+2Cos\beta}{2Cos\beta}=\frac{3Cos\beta}{2Cos\beta}=\frac{3}{2}=1,5\\\\2)-7Sin(\frac{7\pi}{2}-\alpha)=-7Sin(4\pi-(\frac{\pi }{2}+\alpha))=7Sin(\frac{\pi }{2}+\alpha)=7Cos\alpha\\\\Cos\alpha =-\sqrt{1-Sin^{2}\alpha}=-\sqrt{1-(0,28)^{2}}=-\sqrt{1-0,0784}=-\sqrt{0,9216}=-0,96$

$7Cos\alpha =7*(-0,96)=-6,72\\\\3)26Cos(\frac{3\pi }{2}+\alpha)= 26Sin\alpha\\\\Sin\alpha=-\sqrt{1-Cos^{2}\alpha}=-\sqrt{1-(\frac{12}{13})^{2}}=-\sqrt{1-\frac{144}{169}}=-\sqrt{\frac{25}{169}}=-\frac{5}{13}\\\\26Sin\alpha=26*(-\frac{5}{13})=-10$