What is the inverse of sinc(x) or sin(x)/x?

[eddiechai2003]

Homework Statement

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

Homework Equations

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

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?

 

[HallsofIvy]

"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.