Help needed with error propagation problem.

My Mathematics class has been working with error propagation, and I encountered a practice problem that I can't solve.

I tried using the general formula for error propagation that I was given in class : , where c is a function of a and b. However, I keep getting a huge absolute uncertainty of 1000 or so. I would really appreciate if someone could explain how to tackle this. Much thanks.

edit:This is what I'm getting at the moment: • $\frac {\partial c}{\partial \theta}=2A \sin \theta$. It should not be squared under the square root. Only $\sigma_\theta$ should be. That is the factor $\sqrt{200}$ you are out compared to my calculation. – Ross Millikan Jun 24 '17 at 14:20

One check you can do is make the errors go in the direction that will increase $y$ and see how much $y$ changes. The nominal value of $y$ is $100 \cos 90^\circ=0$ If we try to drive $y$ positive, we get $101 \cos 80^\circ \approx 17.54$ so we should be finding an error of about that size.
Your problem is in the $\sigma_\theta$ term. $\theta$ needs to be measured in radians when you take the derivative of the $\cos$ term and in the $\sigma^2_\theta$ term. $\frac{\partial y}{\partial \theta}=2A\sin (2\theta)=200$ $\sigma^2_\theta=\left(\frac {5\pi}{180}\right)^2\approx 0.0076$, so $\sigma_y^2=200\cdot \left(\frac {5\pi}{180}\right)^2\approx 1.52$ The disagreement with the first paragraph is because $y$ is flat at zero at the nominal value. Your equation assumes that things are linear, but here that is a bad approximation.