11.1. Find the set of values of the function $y=|2 \sin x+3 \cos x+4|$.
Answer: $[4-\sqrt{13}, 4+\sqrt{13}]$. Solution. By transforming $2 \sin x+3 \cos x$ using an additional angle $\alpha$, we get $2 \sin x+3 \cos x+4=\sqrt{13} \sin (x+\alpha)+4$. The maximum value of this expression is $4+\sqrt{13}$, and the minimum value is $4-\sqrt{13}>0$. Therefore, the result follows.