tg\alpha=\frac{1}{4}
ctg\alpha=\frac{1}{tg\alpha}
ctg\alpha=\frac{1}{\frac{1}{4}}=4
tg^2\alpha=\frac{sin^2\alpha}{cos^2\alpha}=\frac{1-cos^2\alpha}{cos^2\alpha}=\frac{1}{cos^2\alpha}-1
\frac{1}{cos^2\alpha}-1=(\frac{1}{4})^2
\frac{1}{cos^2\alpha}-1=\frac{1}{16}
\frac{1}{cos^2\alpha}=1+\frac{1}{16}
\frac{1}{cos^2\alpha}=\frac{17}{16}
cos^2\alpha=\frac{16}{17}
cos\alpha=\sqrt{\frac{16}{17}}=\frac{4\sqrt{17}}{17}
sin^2\alpha=1-cos^2\alpha=1-\frac{16}{17}=\frac{1}{17}
sin\alpha=\sqrt{\frac{1}{17}}