1)Oblicz sin x i cos x jeśli :   c)cos (x+¼π) =√5/5 i x ∈(π ; ³/₂π)     2)Narysuj wykres funkcji f(x)= sin(x+|x|)    prosze o wskazówki najpierw rysuje 1. sinx 2...... 3.... .. co dalej??

x to kąt III ćwiartki, więc i sinus, i cosinus są ujemne.   [latex]cos(x+frac{1}{4}pi)=frac{sqrt{5}}{5}\cosx cos(frac{1}{4}pi)-sinx sin(frac{1}{4}pi)=frac{sqrt{5}}{5}\frac{sqrt{2}}{2}(cosx-sinx)=frac{sqrt{5}}{5}\cosx-sinx=frac{sqrt{10}}{5}\cosx=sinx+frac{sqrt{10}}{5}[/latex]   [latex]sin^2x+(sinx+frac{sqrt{10}}{5})^2=1\sin^2x+sin^2x+frac{2sqrt{10}}{5}sinx+frac{2}{5}=1\2sin^2x+frac{2sqrt{10}}{5}sinx-frac{3}{5}=0\Delta=frac{4cdot10}{25}+8cdotfrac{3}{5}=frac{32}{5}[/latex]   [latex]sinx=frac{-frac{2sqrt{10}}{5}-frac{4sqrt{10}}{5}}{4}=-frac{3sqrt{10}}{10} vee sinx=frac{frac{-2sqrt{10}}{5}+frac{4sqrt{10}}{5}}{4}>0\sinx=-frac{3sqrt{10}}{10}[/latex]   [latex]cosx=-frac{3sqrt{10}}{10}+frac{sqrt{10}}{5}=-frac{sqrt{10}}{10}[/latex]