fit data to y~A+B*sin(C*x)

I want to fit discrete data that was measured on a wavegenerator.
In this minimal example i generate some artificial data:

testsin <- 2+ 5 * sin(1:100) #generate sin data
testsin <-  testsin+ rnorm(length(testsin), sd = 0.01) #add noise

mydata <- list(X=1:100, Y=testsin) # generate mydata object

nlmod <- nls(X ~ A+B*sin(C* Y), data=mydata, start=list(A=2, B=4, C=1), trace=TRUE)

# this nls fit fails. 

What do you mean by "fail"

nlmod

Nonlinear regression model
  model:  X ~ A + B * sin(C * Y) 
   data:  mydata 
      A       B       C 
50.7553  0.6308  0.8007 
 residual sum-of-squares: 83308

Number of iterations to convergence: 24 
Achieved convergence tolerance: 7.186e-06 

Results don't seem to look ok.
But I think you made a small mistake in the formula.
The argument to sin in testsin is 1:100 but that's not what you are giving nls.

Try this

nlmod <- nls(Y ~ A+B*sin(C* X), data=mydata, start=list(A=2, B=4, C=1), trace=TRUE)

50.30593 :  2 4 1 
0.01014092 :  2.0003732 5.0002681 0.9999979 
0.01014016 :  2.0003732 5.0002681 0.9999983

nlmod

Nonlinear regression model
  model:  Y ~ A + B * sin(C * X) 
   data:  mydata 
A B C 
2 5 1 
 residual sum-of-squares: 0.01014

Number of iterations to convergence: 2 
Achieved convergence tolerance: 1.201e-07 

Looks better?

Berend