[R] trigonometric regression

[William Simpson]

Suppose I do a trigonometric regression
fit<-lm(y~ cf + sf)
where cf and sf are the cos and sine components.

b<-coef(fit)
I have the fitted sine component b[2] and the cos component b[3].
Doing summary(fit) gives me the p-values and SEs for b[2] and b[3].

But I want the amplitude of the fitted waveform
amp<-sqrt(b[2]^2+b[3]^2)

Can someone please tell me how to get the p-value for amp?

Thanks.
Bill