Найди cos α, если sin α = √3/2

- a) Если $\sin \alpha = \frac{\sqrt{3}}{2}$, то $\cos \alpha = \pm \sqrt{1 - \sin^2 \alpha} = \pm \sqrt{1 - (\frac{\sqrt{3}}{2})^2} = \pm \sqrt{1 - \frac{3}{4}} = \pm \sqrt{\frac{1}{4}} = \pm \frac{1}{2}$. - б) Если $\sin \alpha = \frac{1}{4}$, то $\cos \alpha = \pm \sqrt{1 - \sin^2 \alpha} = \pm \sqrt{1 - (\frac{1}{4})^2} = \pm \sqrt{1 - \frac{1}{16}} = \pm \sqrt{\frac{15}{16}} = \pm \frac{\sqrt{15}}{4}$. - в) Если $\sin \alpha = 0$, то $\cos \alpha = \pm \sqrt{1 - \sin^2 \alpha} = \pm \sqrt{1 - 0^2} = \pm \sqrt{1} = \pm 1$. *Перевод:* - a) If $\sin \alpha = \frac{\sqrt{3}}{2}$, then $\cos \alpha = \pm \sqrt{1 - \sin^2 \alpha} = \pm \sqrt{1 - (\frac{\sqrt{3}}{2})^2} = \pm \sqrt{1 - \frac{3}{4}} = \pm \sqrt{\frac{1}{4}} = \pm \frac{1}{2}$. - б) If $\sin \alpha = \frac{1}{4}$, then $\cos \alpha = \pm \sqrt{1 - \sin^2 \alpha} = \pm \sqrt{1 - (\frac{1}{4})^2} = \pm \sqrt{1 - \frac{1}{16}} = \pm \sqrt{\frac{15}{16}} = \pm \frac{\sqrt{15}}{4}$. - в) If $\sin \alpha = 0$, then $\cos \alpha = \pm \sqrt{1 - \sin^2 \alpha} = \pm \sqrt{1 - 0^2} = \pm \sqrt{1} = \pm 1$.