Задание 317

$-\sin \frac{21\pi}{2}\cdot \cos\left(-\frac{22\pi}{3}\right)=$$-\sin \frac{21\pi}{2}\cdot \cos \frac{22\pi}{3}$

$\frac{21\pi}{2}=\frac{20\pi}{2}+\frac{\pi}{2}=$$10\pi+\frac{\pi}{2}=\frac{\pi}{2}\Rightarrow$

$$\sin\left(10\pi+\frac{\pi}{2}\right)=\sin\frac{\pi}{2}$$

$\frac{22\pi}{3}=\frac{21\pi}{3}+\frac{\pi}{3}=$$7\pi+\frac{\pi}{3} \Rightarrow$

$$\cos\left(7\pi+\frac{\pi}{3}\right)=-\cos\frac{\pi}{3}$$

$-\sin \frac{21\pi}{2}\cdot \cos \frac{22\pi}{3}=$$\sin\frac{\pi}{2}\cdot \left(-\cos\frac{\pi}{3}\right)=$$1\cdot \left(-\frac{1}{2}\right)=-0,5$