Упр.6.4 ГДЗ Мордкович 10-11 класс (Алгебра)

а) t = — 7пи/4;
6) t = — 4пи/3;
в) t = — 5пи/6;
г) t = — 5пи/3.

1. $$t=-\frac{7\pi}{4}$$

   $$\sin t=\sin\left(-\frac{7\pi}{4}\right)=\frac{\sqrt{2}}{2}$$
   
   $$\cos t=\cos\left(-\frac{7\pi}{4}\right)=\frac{\sqrt{2}}{2}$$
   
   $$\tg t=\tg\left(-\frac{7\pi}{4}\right)=1$$

2. $$t=-\frac{4\pi}{3}$$

   $$\sin t=\sin\left(-\frac{4\pi}{3}\right)=\frac{\sqrt{3}}{2}$$
   
   $$\cos t=\cos\left(-\frac{4\pi}{3}\right)=-\frac{1}{2}$$
   
   $$\tg t=\tg\left(-\frac{4\pi}{3}\right)=-\sqrt{3}$$

3. $$t=-\frac{5\pi}{6}$$

   $$\sin t=\sin\left(-\frac{5\pi}{6}\right)=-\frac{1}{2}$$
   
   $$\cos t=\cos\left(-\frac{5\pi}{6}\right)=-\frac{\sqrt{3}}{2}$$
   
   $$\tg t=\tg\left(-\frac{5\pi}{6}\right)=\frac{1}{\sqrt{3}}$$

4. $$t=-\frac{5\pi}{3}$$

   $$\sin t=\sin\left(-\frac{5\pi}{3}\right)=\frac{\sqrt{3}}{2}$$
   
   $$\cos t=\cos\left(-\frac{5\pi}{3}\right)=\frac{1}{2}$$
   
   $$\tg t=\tg\left(-\frac{5\pi}{3}\right)=\sqrt{3}$$

Ответ

а) $$\frac{\sqrt{2}}{2},\ \frac{\sqrt{2}}{2},\ 1$$;
б) $$\frac{\sqrt{3}}{2},\ -\frac{1}{2},\ -\sqrt{3}$$;
в) $$-\frac{1}{2},\ -\frac{\sqrt{3}}{2},\ \frac{1}{\sqrt{3}}$$;
г) $$\frac{\sqrt{3}}{2},\ \frac{1}{2},\ \sqrt{3}$$.