Calculating Uncertainty of an intrinsic function

[sam400]

Homework Statement

I need to calculate the value and the uncertainty of the equation \begin{equation} S = 2d \sin(\theta) \end{equation} (one side of the Bragg formula), however, the final answer is strange, so I would like to know what I'm doing wrong.

Homework Equations

My $\theta$ value: $17.5^{\circ}$
My $d$ value: $4.28 \pm 0.03$ cm
As far as I know, for an intrinsic function, the uncertainty is the root mean squared of the differential, so
\begin{equation} \Delta S = \sqrt{\left(\frac{\partial S}{\partial a} \Delta a \right)^{2} + \left(\frac{\partial S}{\partial b} \Delta b \right)^{2} } \end{equation}

The Attempt at a Solution

After plugging in the numbers and taking the derivatives, the formula that I get is:

\begin{equation}\Delta S = 2 \sqrt{( \sin\theta \Delta d)^{2} + (d \cos\theta \Delta \theta)^2} \end{equation}

For S, I get about 2.60 cm, which is more or less what I expected, but for $\Delta S$, I am getting a value of about 2, which means a relative error of 77%, so there is probably something wrong with what I did.

 

[vela]

What value did you use for $\Delta \theta$?

 

[BvU]

Most frequent error in this context is using degrees instead of radians.

 

[sam400]

Oops, I just realized I have been using degrees for my values. Now my error is more sensible. I had 0.3 degrees for my angle uncertainty, but it wasn't converted to radians.