Вычислите sin t, cos t и tg t, если: 6.4. a) t =$$\frac{-7π}{4}$$; б) t =$$\frac{-4π}{3}$$; в) t =$$\frac{-5π}{6}$$; г) t =$$\frac{-5π}{3}$$. 6.5. a) t =$$\frac{13π}{6}$$; б) t = -$$\frac{8π}{3}$$; в) t =$$\frac{23π}{6}$$; г) t =$$\frac{-11π}{4}$$.

6.4.

a) $$t =\frac{-7\pi}{4}$$

$$sin(-\frac{7\pi}{4}) = sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$$

$$cos(-\frac{7\pi}{4}) = cos(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$$

$$tg(-\frac{7\pi}{4}) = tg(\frac{\pi}{4}) = 1$$

б) $$t =\frac{-4\pi}{3}$$

$$sin(-\frac{4\pi}{3}) = sin(\frac{2\pi}{3}) = \frac{\sqrt{3}}{2}$$

$$cos(-\frac{4\pi}{3}) = -cos(\frac{\pi}{3}) = -\frac{1}{2}$$

$$tg(-\frac{4\pi}{3}) = -tg(\frac{\pi}{3}) = -\sqrt{3}$$

в) $$t =\frac{-5\pi}{6}$$

$$sin(-\frac{5\pi}{6}) = -sin(\frac{\pi}{6}) = -\frac{1}{2}$$

$$cos(-\frac{5\pi}{6}) = -cos(\frac{\pi}{6}) = -\frac{\sqrt{3}}{2}$$

$$tg(-\frac{5\pi}{6}) = tg(\frac{\pi}{6}) = \frac{\sqrt{3}}{3}$$

г) $$t =\frac{-5\pi}{3}$$

$$sin(-\frac{5\pi}{3}) = sin(\frac{\pi}{3}) = \frac{\sqrt{3}}{2}$$

$$cos(-\frac{5\pi}{3}) = cos(\frac{\pi}{3}) = \frac{1}{2}$$

$$tg(-\frac{5\pi}{3}) = \sqrt{3}$$

6.5.

a) $$t =\frac{13\pi}{6}$$

$$sin(\frac{13\pi}{6}) = sin(\frac{\pi}{6}) = \frac{1}{2}$$

$$cos(\frac{13\pi}{6}) = cos(\frac{\pi}{6}) = \frac{\sqrt{3}}{2}$$

$$tg(\frac{13\pi}{6}) = tg(\frac{\pi}{6}) = \frac{\sqrt{3}}{3}$$

б) $$t = -\frac{8\pi}{3}$$

$$sin(-\frac{8\pi}{3}) = -sin(\frac{2\pi}{3}) = -\frac{\sqrt{3}}{2}$$

$$cos(-\frac{8\pi}{3}) = -cos(\frac{\pi}{3}) = -\frac{1}{2}$$

$$tg(-\frac{8\pi}{3}) = \sqrt{3}$$

в) $$t =\frac{23\pi}{6}$$

$$sin(\frac{23\pi}{6}) = -sin(\frac{\pi}{6}) = -\frac{1}{2}$$

$$cos(\frac{23\pi}{6}) = cos(\frac{-\pi}{6}) = \frac{\sqrt{3}}{2}$$

$$tg(\frac{23\pi}{6}) = -tg(\frac{\pi}{6}) = -\frac{\sqrt{3}}{3}$$

г) $$t =\frac{-11\pi}{4}$$

$$sin(-\frac{11\pi}{4}) = -sin(\frac{3\pi}{4}) = -\frac{\sqrt{2}}{2}$$

$$cos(-\frac{11\pi}{4}) = -cos(\frac{\pi}{4}) = -\frac{\sqrt{2}}{2}$$

$$tg(-\frac{11\pi}{4}) = 1$$

Ответ: смотри решение