\[\boxed{\mathbf{1015.ОК\ ГДЗ - домашка\ на}\ 5}\]
\[\textbf{а)}\ cos\ \alpha = 1:\]
\[\text{si}n^{2}\alpha + cos^{2}\alpha = 1\]
\[\sin^{2}\alpha = 1 - \cos^{2}\alpha = 1 - 1 =\]
\[= 0 \Longrightarrow \sin\alpha = 0;\]
\[tg\ \alpha = \frac{\sin\alpha}{\cos\alpha} = \frac{0}{1} = 0.\]
\[\textbf{б)}\ cos\ \alpha = - \frac{\sqrt{3}}{2}:\]
\[\text{si}n^{2}\alpha + cos^{2}\alpha = 1\]
\[\sin^{2}\alpha = 1 - \cos^{2}\alpha = 1 - \frac{3}{4} = \frac{1}{4}\]
\[\sin\alpha = \pm \frac{1}{2}.\]
\[tg\ \alpha = \frac{\sin\alpha}{\cos\alpha} = \pm \frac{1}{2}\ :\left( - \frac{\sqrt{3}}{2} \right) =\]
\[= \pm \frac{\sqrt{3}}{3}.\]
\[\textbf{в)}\ sin\ \alpha = \frac{\sqrt{2}}{2};\ 0{^\circ} < \alpha < 90{^\circ}:\]
\[\text{si}n^{2}\alpha + cos^{2}\alpha = 1\]
\[\cos^{2}\alpha = 1 - \sin^{2}\alpha = 1 - \frac{2}{4} =\]
\[= \frac{2}{4} \Longrightarrow \cos\alpha = \pm \frac{\sqrt{2}}{2};\]
\[0{^\circ} < \alpha < 90{^\circ};\ \]
\[\text{cos\ }\alpha > 0 \Longrightarrow \cos\alpha = \frac{\sqrt{2}}{2};\ \]
\[tg\ \alpha = \frac{\sin\alpha}{\cos\alpha} = \frac{\sqrt{2}}{2}\ :\frac{\sqrt{2}}{2} = 1.\]
\[\textbf{г)}\ sin\ \alpha = \frac{3}{5};\ 90{^\circ} < \alpha < 180{^\circ}:\]
\[\text{si}n^{2}\alpha + cos^{2}\alpha = 1\]
\[\cos^{2}\alpha = 1 - \sin^{2}\alpha = 1 - \frac{9}{25} =\]
\[= \frac{16}{25} \Longrightarrow \cos\alpha = \pm \frac{4}{5};\]
\[90{^\circ} < \alpha < 180{^\circ};\ \]
\[\text{cos\ }\alpha < 0 \Longrightarrow \cos\alpha = - \frac{4}{5};\ \]
\[tg\ \alpha = \frac{\sin\alpha}{\cos\alpha} = \frac{3}{5}\ :\left( - \frac{4}{5} \right) = - \frac{3}{4}.\]