Question

TgA=7/24 и 180< A<270. найдите cosA

Answer 1

$\\cos\alpha<0 \\\frac{sin\alpha}{cos\alpha}=\frac{7}{24}\implies \ sin\alpha=\frac{7}{24}*cos\alpha \\sin^2\alpha+cos^2\alpha=1 \\(\frac{7}{24})^2+cos^2\alpha=1 \\\frac{625}{576}cos^2\alpha=1 \\cos\alpha=-\sqrt{\frac{576}{625}} \\cos\alpha=-\frac{24}{25}$