9. Find the maximum value of the function $f(x)=5 \sin x+12 \cos x$.
Solution: $f(x)=5 \sin x+12 \cos x=\sqrt{5^{2}+12^{2}}\left(\sin \left(x+\operatorname{arctg} \frac{12}{5}\right)\right)=\sqrt{13^{2} \sin x}$.

Answer: 13 .