Is the following graph of the function $f(x) = \ln (2\sin \frac{x}{2})$ right?

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In my text book about Fourier Analysis, $x$ ranges from $-\pi$ to $\pi$.I think when $x$ is from $-\pi$ to $0$, $\displaystyle \ln(2\sin\frac{x}{2})$ is meaningless. Why does the left part of the figure exist?