Kąt alfa jest rozwarty i tangens alfa = -5/12. Oblicz cosinus alfa.

[latex]tg \alpha=- \frac{5}{12}\\ \\ \frac{sin \alpha}{cos \alpha}=- \frac{5}{12}|^2\\ \\\frac{sin^2 \alpha}{cos^2 \alpha}=\frac{25}{144}\\ \\\frac{1-cos^2 \alpha}{cos^2 \alpha}=\frac{25}{144}\\ \\\frac{1}{cos^2 \alpha}-1=\frac{25}{144}\\ \\\frac{1}{cos^2 \alpha}=\frac{169}{144}\\ \\cos^2 \alpha= \frac{144}{169}\\ \\cos \alpha = \frac{12}{13} [/latex]