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$tg \alpha = \frac{sin \alpha }{cos \alpha }$
$ctg \alpha = \frac{cos \alpha }{sin \alpha }$
$sin^2 \alpha +cos^2 \alpha =1$
$cos^2 \alpha =1-sin^ \alpha =1- \frac{576}{625}= \frac{49}{625}$
$cos \alpha =$ ± $\sqrt{ \frac{49}{625} } =$ ± $\frac{7}{25}$
так как $\frac{ \pi }{2}$ <α < π α∈II четверти, то<br>cosα=- $\frac{7}{25}$
$tg \alpha = \frac{24}{25} *(- \frac{25}{7} )=- \frac{24}{7}$
$ctg \alpha =- \frac{7}{25} * \frac{25}{24}=- \frac{7}{24}$