# How to find error in trigonometric ratios?

How do I find the error in measurement of $\sin \theta$, if I am given the error in the measurement of the $\theta$

In general, if you have a function $f$ of a single variable $x$, you can propagate the uncertainty in the following way: $$\delta f = \left|\frac{df}{dx}\right| \delta x$$

If you have a function $g$ of several variables $x$ and $y$ with uncorrelated uncertainties, then $$\delta g = \sqrt{\left(\frac{\partial g}{\partial x}\cdot \delta x\right)^2 + \left(\frac{\partial g}{\partial y}\cdot \delta y\right)^2}$$

If your uncertainties are correlated ... you have more work to do ;)