[latex]3sinalpha-5cosalpha=0\ 3sinalpha=5cosalpha\ sinalpha=frac53cosalpha\ \ sin^2alpha+cos^2alpha=1\ (frac53cosalpha)^2+cos^2alpha=1\ frac{25}{9}cos^2alpha+cos^2alpha=1\ frac{34}{9}cos^2alpha=1\ cos^2alpha=frac{9}{34}\ \ cosalpha=sqrt{frac{9}{34}}\ cosalpha=frac{3}{sqrt{34}}\ cosalpha=frac{3sqrt{34}}{34}\ \ [/latex] [latex]sinalpha=frac53cdotfrac{3sqrt{34}}{34}\ sinalpha=frac{5sqrt{34}}{34}[/latex] Sprawdzenie: [latex]3cdotfrac{5sqrt{34}}{34}-5cdotfrac{3sqrt{34}}{34}=frac{15sqrt{34}}{34}-frac{15sqrt{34}}{34}=0[/latex]
