Question

how do I carry an experimental error through an arcsine?

Answer 1

I have \[tan^{-1}\left(\frac{19mm}{47mm\pm 1mm}\right)\]

Answer 2

and want angle \(\pm\) error

Answer 3

When determining an error in a function of several variables when you know the error in the variables take the derivative of the function with respect to each and use \[\Delta f=\sqrt{\sum_{1}^{i}\left( \frac{ df }{dx _{i} } \right)^{2}_{x _{i}}\Delta x _{i} ^{2} } \] where delta x is the known error in xi and the derivative is evaluated at the current value of xi.