# Calculating the overall uncertainty of my measurements

• cosmicaa

## Homework Statement

I conducted an experiment to find the refractive index of several concentrations of sugar solutions. I now need to find out the final uncertainty of my measurements but am unsure of how to go about calculating it.

## Homework Equations

• I took 2 measurements of length which i estimate the uncertainty to be +/- 0.025cm (let these measurements of length be a & b)
• I divided these two lengths and took the arctan of them: c=arctan(a/b)
• I then placed it in this equation: 2sin(c/2+pi/6)

What happens to the uncertainty?

## The Attempt at a Solution

I am not too sure with the trigonometric operators but I assume they don't do anything to the uncertainties. I am guessing that if this is true, then i just use the usual uncertainty rules of +, -, /, * ?

Thanks so much!

If you don't know, or forget, the rules governing this, there is a simple way of finding out the maximum uncertainty in your calculated answer based on single measurements.
Find the highest possible value of c using (a + uncertainty) divided by (b - uncertainty) then the lowest value by reversing the + and -
Then put those two values into your sin expression to find the highest and lowest possible values of that.