Tgt=-5/12 п/2 Найти sinT cosT ctgT

Решите задачу:

$tgt=- \frac{5}{12} \\\\ \frac{\pi}{2}\ \textless \ t\ \textless \ \pi \; \; \; \to \; \; \; sint\ \textgreater \ 0\; ,\; \; cost\ \textless \ 0\; ,\; \; ctgt\ \textless \ 0\\\\1+tg^2t= \frac{1}{cos^2t} \; \; \to \; \; cos^2t= \frac{1}{1+tg^2t} \\\\cos^2t= \frac{1}{1+25/144} = \frac{144}{169} \; \; \to \; \; cost=- \frac{12}{13} \\\\sin^2t=1-cos^2t=1- \frac{144}{169} = \frac{25}{169} \; \; \to \; \; \; sint= \frac{5}{13} \\\\ctgt=\frac{cost}{sint}=- \frac{12}{13} :\frac{5}{13} =- \frac{12}{5}$