Finding Uncertainty of Theta from Slope 'a' Uncertainty

[Shaddyab]

I am running a test where I start by preforming a calibration to fit the following linear line

V= a * X + b

where: X is Displacement, and V is Voltage reading.

Then, I acquire my data where I measure V and find X based on X = V/a ( the b drops down ), and find an angle Theta = X/f such that Theta = V/(a*f)

My questions is:

If I know that the uncertainty of the slope 'a' is

where

How can I find the uncertainty of Theta?


Thank you

 

[EnumaElish]

var theta = var(X/(a*f)) = var(X/a)/f^2. The simple approach is to assume X is given (e.g., X = sample mean). Then var(X/a)/f^2 = var(1/a)(X/f)^2 and use http://en.wikipedia.org/wiki/Variance#Approximating_the_variance_of_a_function for var(1/a).