How can I get all possible solutions for an equation?

I need to get all possible solutions for this equation:

   sin(x)/x == a

for "0.2 < a < 1", it has 3 to 5 solutions but matlab functions such as "solve" and "vpasolve" only return the first solution they find. How can I get all the answers? should I use another function?

thank you all payman

Answer 1

[Greg Heath]

Some or all of the solutions can probably be obtained via recursion.

Given a, b=1/a and x(1), try

 x(n+1) = arcsin(a*x(n))
and
 x(n+1) = b*sin(x(n))

Simultaneously plotting y1= a*x and y2 = sin(x) for 0.2 <= a <= 1 will yield insight.

Hope this helps.

Thank you for formally accepting my answer

Greg

[payman khayree]

not what I was looking for, but anyways thanks for your answers

Answer 2

[John D'Errico]

All possible solutions is in general an impossible thing for a completely general function, since there may be infinitely many such solutions.

If you know there are a finite number of solutions, and can bound them, then just sample your function on a fine enough interval, and use fzero over brackets generated by the sampling. WTP?