9. Find the maximum value of the function $f(x)=3 \sin x+4 \cos x$.
Solution: $f(x)=3 \sin x+4 \cos x=\sqrt{3^{2}+4^{2}} \sin \left(x+\operatorname{arctg} \frac{4}{3}\right)=5 \sin \left(x+\operatorname{arctg} \frac{4}{3}\right)$.

Answer: The maximum value is 5.