# Inverse of sinc

1. Jan 5, 2009

### eddiechai2003

1. The problem statement, all variables and given/known data

Does anyone know the inverse of $$sinc(x)$$ or $$\frac{sin(x)}{x}$$?

2. Relevant equations

If $$sinc(x)=a$$, $$x=f(a)$$. What is $$x$$ in function of $$a$$?

3. The attempt at a solution

If I knew the exact value of $$a$$, I could find the corresponding value of $$x$$ graphically. But how do I find $$x$$ if I didn't know $$a$$?

Last edited: Jan 5, 2009
2. Jan 5, 2009

### HallsofIvy

Staff Emeritus
"sin(x)" itself does not have a true inverse. If you restrict x to between 0 and $\pi$, sin(x) and sinc(x) have inverses but the inverse of sinc(x) cannot be written in terms of simple functions. If y= sinc(x)= sin(x)/x, then finding the inverse function would be the same as solving xy= sin(x) for x which cannot be done in terms of simple functions.