trigonometry - sinc function centered at $x=c$ that goes to zero at $x=0$?

The sinc function is ordinarily defined as

$$
\operatorname{sinc}(x) = \frac{\sin x} x \text{ if } x \neq 0 \text{ else } 1.
$$

I want a sinc function that is shifted away from the origin such that it's centered at some value $c$, and also equals zero at $x=0$. How can I define this function?