Error Propagation in Trigonometric Functions

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Homework Help Overview

The discussion revolves around calculating error propagation in trigonometric functions, specifically focusing on the tangent function and its relationship with uncertainty in angle measurements.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster expresses uncertainty about applying error propagation to the tangent function despite understanding it for basic functions. Some participants suggest using the Tan(A+B) formula and differentiating to find the error. Others discuss the implications of using a first-order approximation for non-zero errors.

Discussion Status

Participants are exploring various methods to approach the problem, including differentiation and referencing external resources. There is an ongoing exchange of ideas without a clear consensus on the best method to apply.

Contextual Notes

The original poster indicates familiarity with error analysis for basic functions but seeks clarification specifically for trigonometric functions, suggesting a potential gap in understanding or resources available for this topic.

H_man
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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 [tex]\theta[/tex] 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.
 
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First thing come to my mind is to use the Tan(A+B) formula..
ps:did you try to differentiate?Tan(A+Delt(A))??
 
Last edited:
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
 
Last edited:
ziad1985 said:
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.
 
Are you asking for propagation of error?
Have a look at here:
http://www.rit.edu/~uphysics/uncertainties/Uncertaintiespart2.html#functions2
 
Last edited by a moderator:

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