x- długość drugiej przyprostokątnej [latex]x^2+4^2=12^2\x^2=144-16=128\x=8sqrt{2}[/latex] [latex]sinalpha=coseta=frac{4}{12}=frac{1}{3}\sineta=cosalpha=frac{8sqrt{2}}{12}=frac{2sqrt{2}}{3}[/latex] b) [latex]cos2eta=2cos^2eta-1=2cdot(frac{1}{3})^2-1=frac{2}{9}-1=-frac{7}{9}[/latex] c) [latex]sin(eta-alpha)=sineta cosalpha-sinalpha coseta=(frac{2sqrt{2}}{3})^2-(frac{1}{3})^2=frac{8}{9}-frac{1}{9}=frac{7}{9}[/latex] d) [latex]cos(alpha-eta)=cosalpha coseta+sinalpha sineta=frac{2sqrt{2}}{3}cdotfrac{1}{3}+frac{2sqrt{2}}{3}cdotfrac{1}{3}=frac{4sqrt{2}}{9}[/latex]
