1013 Найдите sin a, если: a) cos α = 1 2 ; б) cos α = −2 3 ; в) cos α = −1.

a) cos α = $$\frac{1}{2}$$

$$\sin^2 α + \cos^2 α = 1$$

$$\sin α = \pm \sqrt{1 - \cos^2 α}$$

$$\sin α = \pm \sqrt{1 - (\frac{1}{2})^2} = \pm \sqrt{1 - \frac{1}{4}} = \pm \sqrt{\frac{3}{4}} = \pm \frac{\sqrt{3}}{2}$$

б) cos α = -$$\frac{2}{3}$$

$$\sin α = \pm \sqrt{1 - (-\frac{2}{3})^2} = \pm \sqrt{1 - \frac{4}{9}} = \pm \sqrt{\frac{5}{9}} = \pm \frac{\sqrt{5}}{3}$$

в) cos α = -1

$$\sin α = \pm \sqrt{1 - (-1)^2} = \pm \sqrt{1 - 1} = 0$$

Ответ: a) $$\pm \frac{\sqrt{3}}{2}$$; б) $$\pm \frac{\sqrt{5}}{3}$$; в) $$0$$