1) dla tgα=60/11
[tex]tg\alpha=\frac{60}{11}\\\\tg^2\alpha=\frac{sin^2\alpha}{cos^2\alpha}\\sin^2\alpha=1-cos^2\alpha\\\\\frac{3600}{121}=\frac{1-cos^2\alpha}{cos^2\alpha}\\3600cos^2\alpha=121-121cos^2\alpha\\3721cos^2\alpha=121 /:3721\\cos^2\alpha=\frac{121}{3721}\\cos\alpha=\frac{11}{61}\\\\sin^2\alpha=1-\frac{121}{3721}\\sin^2\alpha=\frac{3600}{3721}\\sin\alpha=\frac{60}{61}[/tex]
[tex]ctg\alpha=\frac{1}{tg\alpha}=1*\frac{11}{60}\\ctg\alpha=\frac{11}{60}[/tex]
2) dla tgα=2
[tex]tg^2\alpha=4\\4=\frac{1-cos^2\alpha}{cos^2\alpha}\\4cos^2\alpha=1-cos^2\alpha\\5cos^2\alpha=1 /:5\\cos^2\alpha=\frac15\\cos\alpha=\sqrt{\frac15}=\frac{1}{\sqrt5}=\frac{\sqrt5}5\\\\sin^2\alpha=1-\frac15\\sin^2\alpha=\frac45\\sin\alpha=\frac{2}{\sqrt5}=\frac{2\sqrt5}5\\\\ctg\alpha=\frac1{tg\alpha}=\frac12[/tex]
