5. The graph of the function $f(x)=\sin x+2|\sin x|, x \in[0,2 \pi]$ intersects the line $y=k$ at exactly two distinct points, then the range of values for $k$ is
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Answer $1<k<3$.
Analysis $f(x)=\left\{\begin{array}{ll}3 \sin x, & x \in[0, \pi] \\ -\sin x, & x \in(\pi, 2 \pi]\end{array}\right.$, by plotting its graph, we can see that the range of $k$ for which there are two intersection points is $1<k<3$.