Найти cos α , ctg α если sin α = 0,8

cos^{2} α=1- sin^{2} α cos α=0.9 ctg α=cos α/sin α ctg α=1.125

[latex]sin^2\alpha+cos^2\alpha=1[/latex], значит [latex]cos^2\alpha=1-sin^2\alpha[/latex], а тогда [latex]cos\alpha=\sqrt{1-sin^2\alpha}=\sqrt{1-0,8^2}=\sqrt{1-0,64}=\sqrt{0,36}=0,6[/latex];  [latex]1+ctg^2\alpha=\frac{1}{sin^2\alpha}[/latex], значит [latex]ctg^2\alpha=\frac{1}{sin^2\alpha}-1=\frac{1}{sin^2\alpha}-\frac{sin^2\alpha}{sin^2\alpha}=\frac{1-sin^2\alpha}{sin^2\alpha}=\frac{cos^2\alpha}{sin^2\alpha}[/latex], а тогда [latex]ctg\alpha=\sqrt{\frac{cos^2\alpha}{sin^2\alpha}}=\frac{cos\alpha}{sin\alpha}=\frac{0,6}{0,8}=0,75[/latex]