Question

Вычислите значение cos a, если ctg a=- 18/15 и π/2<a<π​

Answer 1

$Ctg\alpha=-\frac{18}{15}\\\\\frac{\pi }{2} < \alpha <\pi$

α - угол второй четверти, значит Cosα < 0 .

$tg\alpha=\frac{1}{Ctg\alpha}=-\frac{1}{\frac{18}{15}}=-\frac{15}{18}\\\\1+tg^{2}\alpha=\frac{1}{Cos^{2}\alpha}\\\\Cos^{2} \alpha=\frac{1}{1+tg^{2}\alpha}=\frac{1}{1+(-\frac{15}{18})^{2}}=\frac{1}{1+\frac{225}{324}}=\frac{1}{\frac{549}{324}}=\frac{324}{549}\\\\Cos\alpha=-\sqrt{\frac{324}{549} }=-\frac{18}{3\sqrt{61}}=-\frac{6}{\sqrt{61}}$