Error Propagation in Trigonometric Functions

[H_man]

Homework Statement

I can't seem to find online how to calculate the error propogated by trigonometric functions.

That is, I know the uncertainty in $$\theta$$ but am not sure how to deal with it when I apply the tan function.

I am quite okay with how to deal with all the basic functions w.r.t. error analysis, just not the trig ones.

Homework Equations

misc * tan(theta)

The Attempt at a Solution

Searched the internet.

 

[ziad1985]

First thing come to my mind is to use the Tan(A+B) formula..
ps:did you try to differentiate?Tan(A+Delt(A))??

 

[ziad1985]

what I mean by differentiate is this:
Tan(x+dx)=Tan'(x)dx + tan(x)
Edit:the above formula is derived from the definition of derivation, thus the error would be Tan'(x)dx

 

[HallsofIvy]

what I mean by differentiate is this:
Tan(x+dx)=Tan'(x)dx + tan(x)
Edit:the above formula is derived from the definition of derivation, thus the error would be Tan'(x)dx

Minor point: that is true in the limit as dx goes to 0. For non-zero error dx, it is a first order approximation to the error in the function. That's probably what is needed here.

 

[Edgardo]

Are you asking for propagation of error?
Have a look at here:
http://www.rit.edu/~uphysics/uncertainties/Uncertaintiespart2.html#functions2