9. Find the maximum value of the function $f(x)=8 \sin x+15 \cos x$.
Solution: $f(x)=8 \sin x+15 \cos x=\sqrt{8^{2}+15^{2}} \sin \left(x+\operatorname{arctg} \frac{15}{8}\right)=17 \sin \left(x+\operatorname{arctg} \frac{15}{8}\right)$

Answer: The maximum value of $f(x)=17$.