[latex]sinalpha=frac{4}{5}[/latex] [latex](frac{4}{5})^2+cos^2alpha=1\cos^2alpha=1-frac{16}{25}=frac{9}{25}\cosalpha=frac{3}{5}[/latex] [latex]tgalpha=frac{sinalpha}{cosalpha}=frac{frac{4}{5}}{frac{3}{5}}=frac{4}{3}[/latex] [latex]ctgalpha=frac{1}{tgalpha}=frac{3}{4}[/latex]
[latex]sin^{2} alpha +cos^{2} alpha =1 \ \ ( frac{4}{5}) ^{2} +cos^{2} alpha =1 \ \ cos^{2} alpha =1- frac{16}{25} \ \ cos^{2} alpha = frac{9}{25} \ \ cos alpha >0, czyli cos alpha = frac{3}{5}[/latex] [latex]tg alpha = frac{sin alpha }{cos alpha } = frac{4}{5}:frac{3}{5}=frac{4}{5}cdotfrac{5}{3}=frac{4}{3} \ \ ctg alpha = frac{1}{tg alpha } =frac{3}{4}[/latex]
