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.