9. Solve the equation $9 \sin x - 12 \cos x = 15$.
Solution:

$$
9 \sin x-12 \cos x=15, \sqrt{9^{2}+12^{2}} \sin \left(x-\operatorname{arctg} \frac{4}{3}\right)=15
$$

$$
\sin \left(x-\operatorname{arctg} \frac{4}{3}\right)=1, x-\operatorname{arctg} \frac{4}{3}=\frac{\pi}{2}+2 \pi k, x=\operatorname{arctg} \frac{4}{3}+\frac{\pi}{2}+2 \pi k
$$