If the measurement of an object is in the form $\sin(\theta)=.256 \pm.004$, how do we calculate the error of $\theta$?
Using the computational method for $\sin(\theta)=\frac{H}{L}$, for $H=.254$ ,$\delta_H=.001$, $L=.992$ and $\delta_L=.001$, I get
$$\delta_{\sin\left(\theta\right),H}=\frac{H+\delta_H}{L}-\frac{H}{L}=.004....$$
and
$$\delta_{\sin\left(\theta\right),L}=\frac{H}{L+\delta_{L}}-\frac{H}{L}=.255...$$
I want to calculate $\delta_{\theta,H}$ and $\delta_{\theta,L}$ to get $\delta_{\theta}=\sqrt{\left(\delta_{\theta,H}\right)^2+\left(\delta_{\theta,L}\right)^2}=$
I looked online but could not find an answer. My assumption is too take $\pm\sin^{-1}(.004)$ but I have feeling this is incorrect.