11) Найдите: a) sin 855°; 6)tg \frac{34π}{3}.

Ответ: a) \(\frac{\sqrt{2}}{2}\); б) \(-\sqrt{3}\)

Решение:

• а) \(\sin(855^\circ)\):
  • \(\sin(855^\circ) = \sin(855^\circ - 2 \cdot 360^\circ) = \sin(855^\circ - 720^\circ) = \sin(135^\circ)\)
  • \(\sin(135^\circ) = \sin(180^\circ - 45^\circ) = \sin(45^\circ) = \frac{\sqrt{2}}{2}\)
• б) \(\tan(\frac{34\pi}{3})\):
  • \(\tan(\frac{34\pi}{3}) = \tan(\frac{34\pi}{3} - 5 \cdot 2\pi) = \tan(\frac{34\pi}{3} - \frac{30\pi}{3}) = \tan(\frac{4\pi}{3})\)
  • \(\tan(\frac{4\pi}{3}) = \tan(\pi + \frac{\pi}{3}) = \tan(\frac{\pi}{3}) = \sqrt{3}\)

Ответ: a) \(\frac{\sqrt{2}}{2}\); б) \(\sqrt{3}\)