1016 Вычислите синусы, косинусы и тангенсы углов 120°, 135°, 150°.

1016.

• 120° = 180° - 60°. sin 120° = sin (180° - 60°) = sin 60° = $$\frac{\sqrt{3}}{2}$$. cos 120° = -cos 60° = -$$\frac{1}{2}$$. tg 120° = -tg 60° = -$$\sqrt{3}$$.


• 135° = 180° - 45°. sin 135° = sin (180° - 45°) = sin 45° = $$\frac{\sqrt{2}}{2}$$. cos 135° = -cos 45° = -$$\frac{\sqrt{2}}{2}$$. tg 135° = -tg 45° = -1.


• 150° = 180° - 30°. sin 150° = sin (180° - 30°) = sin 30° = $$\frac{1}{2}$$. cos 150° = -cos 30° = -$$\frac{\sqrt{3}}{2}$$. tg 150° = -tg 30° = -$$\frac{\sqrt{3}}{3}$$.

Ответ: sin 120° = $$\frac{\sqrt{3}}{2}$$, cos 120° = -$$\frac{1}{2}$$, tg 120° = -$$\sqrt{3}$$; sin 135° = $$\frac{\sqrt{2}}{2}$$, cos 135° = -$$\frac{\sqrt{2}}{2}$$, tg 135° = -1; sin 150° = $$\frac{1}{2}$$, cos 150° = -$$\frac{\sqrt{3}}{2}$$, tg 150° = -$$\frac{\sqrt{3}}{3}$$.