Cosa,sin a/2=24/25,pi/2<a<pi

$sin \alpha = \frac{24}{25} , \frac{ \pi }{2} \ \textless \ \alpha\ \textless \ \pi$

основное тригонометрическое тождество:

sin²α+cos²α=1

$(\frac{24}{25}) ^{2}+ cos^{2} \alpha =1$
$cos^{2} \alpha = \frac{49}{625}$
cosα<0, т.к по условию <img src="https://tex.z-dn.net/?f=+%5Cfrac%7B+%5Cpi+%7D%7B2%7D+%5C+%5Ctextless+%5C++%5Calpha+%5C+%5Ctextless+%5C++%5Cpi+" id="TexFormula4" title=" \frac{ \pi }{2} \ \textless \ \alpha \ \textless \ \pi " alt=" \frac{ \pi }{2} \ \textless \ \alpha \ \textless \ \pi " align="absmiddle" class="latex-formula">

$\alpha =- \frac{7}{25}$