# Calculating uncertainty

1. Apr 15, 2008

### questions

I have a lab where I have to calculate the theoretical value of R using the following equation and then find the uncertainty in R.

R=(xCOS(y))*((-xSIN(y)-SQRT((xSIN(y))^2-2*-9.8*z))/-9.8)
*I know the values of x,y,z and their respective uncertainties.

The problem is that we have only learned basic uncertainty rules (i.e. for multiplication/division you add the %uncertainty, for addition/subtraction you add the absolute uncertainties). This is much more complicated since I have to deal with SIN/COS and square roots. I was searching around and it seems that I have to calculate the partial derivative or differentials. I am not familiar with differentials and I have no idea how to solve this problem. If anyone can offer any help whatsoever it would be greatly appreciated or anywhere where I can find this information.

2. Apr 15, 2008

### questions

I'm using excel if that makes any difference whatsoever

3. Apr 17, 2008

### n0_3sc

You are quite right about using partial derivatives. Don't be scared yet. I agree that you have a complicated expression to start with. I would suggest first simplifying it as much as possible (using trig identities). I assume you know basic differentiation? I really hope so...
When I say "simplify" I mean put it in a form thats less "scary" to differentiate. (derivatives of sin and cos can be found in any table of derivatives).

Example: If you have a function $$T=T(f,\lambda,...)$$ then the error in T is found by:
$$(\delta T)^2 = (\frac{dT}{df})^2(\delta f)^2 + (\frac{dT}{d\lambda})^2(\delta \lambda)^2+(\frac{dT}{d...})^2(\delta ...)^2$$
where $$\delta$$ is the error value(s).

4. Apr 17, 2008

### n0_3sc

I don't know if Excel can differentiate...Ever used Matlab or Mathematica?

5. Apr 17, 2008

### Phlogistonian

To calculate the partial derivative $\partial R/\partial x$, differentiate R with respect to x, treating all the other variables as constants. Do likewise for the other partial derivatives.

Last edited: Apr 17, 2008