1014 Найдите cos а, если: a) sin x = √3 2 ; б) sina = 1 4 ; в) sin a = 0.

a) sin α = $$\frac{\sqrt{3}}{2}$$

$$\cos^2 α + \sin^2 α = 1$$

$$\cos α = \pm \sqrt{1 - \sin^2 α}$$

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

б) sin α = $$\frac{1}{4}$$

$$\cos α = \pm \sqrt{1 - (\frac{1}{4})^2} = \pm \sqrt{1 - \frac{1}{16}} = \pm \sqrt{\frac{15}{16}} = \pm \frac{\sqrt{15}}{4}$$

в) sin α = 0

$$\cos α = \pm \sqrt{1 - 0^2} = \pm 1$$

Ответ: a) $$\pm \frac{1}{2}$$; б) $$\pm \frac{\sqrt{15}}{4}$$; в) $$ \pm 1$$