\[\boxed{\mathbf{1014.ОК\ ГДЗ - домашка\ на}\ 5}\]
\[\textbf{а)}\ sin\ \alpha = \frac{\sqrt{3}}{2}:\]
\[\text{si}n^{2}\alpha + cos^{2}\alpha = 1\]
\[\cos^{2}\alpha = 1 - \sin^{2}\alpha = 1 - \frac{3}{4} = \frac{1}{4}\]
\[\cos\alpha = \pm \frac{1}{2}.\]
\[\textbf{б)}\ sin\ \alpha = \frac{1}{4}:\]
\[\text{si}n^{2}\alpha + cos^{2}\alpha = 1\]
\[\cos^{2}\alpha = 1 - \sin^{2}\alpha = 1 - \frac{1}{16} =\]
\[= \frac{15}{16}\]
\[\cos\alpha = \pm \frac{\sqrt{15}}{4}.\]
\[\textbf{в)}\ sin\ \alpha = 0:\]
\[\text{si}n^{2}\alpha + cos^{2}\alpha = 1\]
\[\cos^{2}\alpha = 1 - \sin^{2}\alpha = 1 - 0 = 1\]
\[\cos\alpha = \pm 1.\]