Robust nonlinear regression - sin(x)/x?

Dear all

Since I did not receive any answer to my general question (?),
let me ask a concrete question:

How can I fit the simple function y = a*sin(x)/b*x?

This is the code that I tried, but nls gives an error:

x <- seq(1,10,0.1)
y <- sin(x)/x
plot(x,y)
z <- jitter(y,amount=0.1)
plot(x,z)
df <- as.data.frame(cbind(x,z))
nf <- nls(z ~ a*sin(x)/b*x, data=df,
           start=list(a=0.8,b=0.9), trace = TRUE)

I have followed the Puromycin sample which works fine:
Pur.wt <- nls(rate ~ (Vm * conc)/(K + conc), data = Treated,
               start = list(Vm = 200, K = 0.1), trace = TRUE)

Do I make some mistake or is it not possible to fit sin(x)/x?