[tex]a)\\sin\alpha=\frac13\\sin^2\alpha+cos^2\alpha=1\\(\frac13)^2+cos^2\alpha=1\\\frac19+cos^2\alpha=1\\cos^2\alpha=1-\frac19\\cos^2\alpha=\frac89\\cos\alpha=\sqrt{\frac89}=\frac{2\sqrt2}3\\tg\alpha=\frac{sin\alpha}{cos\alpha}\\tg\alpha=\frac13*\frac3{2\sqrt2}=\frac{1}{2\sqrt2}=\frac{\sqrt2}{2*2}=\frac{\sqrt2}4\\ctg\alpha=\frac4{\sqrt2}=\frac{4\sqrt2}2=2\sqrt2[/tex]
[tex]b) \\tg\alpha=\sqrt3\\tg\alpha=\frac{sin\alpha}{cos\alpha}\\\sqrt3=\frac{sin\alpha}{cos\alpha}\\\sqrt3cos\alpha=sin\alpha\\sin^2\alpha+cos^2\alpha=1\\(\sqrt3cos\alpha)^2+cos^2\alpha=1\\3cos^2\alpha+cos^2\alpha=1\\4cos^2\alpha=1/:4\\cos^2\alpha=\frac14\\cos\alpha=\sqrt{\frac14}=\frac12\\ctg\alpha=\frac1{\sqrt3}=\frac{\sqrt3}3[/tex]
