Mam problem z zadaniem: Oblicz cos 11π/60 jeżeli sin π/15=a Doszedłem do tego: Ponieważ 11π/60+π/15=π/4, więc sin(π/15+11π/60)=sin π/4=√2/2 Korzystam z wzoru na sumę sinusów: sin(π/15+11π/60)=√2/2= sin π/15 cos 11π/60+cos π/15 sin 11π/60 √2/2= a∙co

[latex]frac{11}{60}pi=frac{15}{60}pi-frac{4}{60}pi=frac{pi}{4}-frac{pi}{15}[/latex] [latex]sin{frac{pi}{15}}=a\cos{frac{pi}{15}}=sqrt{1-a^2}[/latex] [latex]cos{frac{11}{60}pi}=cos(frac{pi}{4}-frac{pi}{15})=\=cos{frac{pi}{4}}cdot cos{frac{pi}{15}}+sin{frac{pi}{4}}cdot sin{frac{pi}{15}}=\=frac{sqrt{2}}{2}cdotsqrt{1-a^2}+frac{sqrt{2}}{2}cdot a=frac{sqrt{2}}{2}(a+sqrt{1-a^2})[/latex]

[latex]cosfrac{11pi}{60}=cos(frac{pi}{4}-frac{pi}{15})=cosfrac{pi}{4}cdotcosfrac{pi}{15}+sinfrac{pi}{4}cdotsinfrac{pi}{15}=\\=frac{sqrt{2}}{2}cdotsqrt{1-a^2}+frac{sqrt{2}}{2}cdot{}a=frac{sqrt{2}}{2}cdot(a+sqrt{1-a^2})[/latex]