Answer:
[tex]sin \theta = - \frac{1}{5}[/tex]
Step-by-step explanation:
We Know
[tex]sin ^2 \theta + cos^2 \theta = 1\\[/tex]
[tex]sin^2 \theta = 1 - cos^2 \theta[/tex]
[tex]= 1 - (-\frac{\sqrt{24} }{5})^2[/tex] [tex][\ given : cos \theta = -\frac{\sqrt{24} }{5} \ ][/tex]
[tex]= 1 - \frac{24}{25}\\\\= \frac{25 - 24}{25}\\\\=\frac{1}{25}[/tex]
[tex]sin ^2 \theta = \frac{1}{25}\\\\sin \theta = \sqrt {\frac{1}{25}}\\\\sin \theta = \pm \frac{1}{5}\\\\Since \ \theta \ is \ in \ III \ Quadrant \ sin \theta = -\frac{1}{5}[/tex]
