I've been searching all over the net and I can't seem to find a definitive answer - perhaps I'm asking the wrong question.
How does one calculate the relative error (%) of the cos/sin/tan of an angle in degrees?
So, let's say that I have an angle of 30 degrees with an absolute error of ±2. The absolute error of the sin of 30 degrees would be:
$sin (30+2)-sin(30) = 0.0299 $
Now what do I do to obtain the relative error?
By definition relative error is given by $\delta f / f$ so f here is sin30 and the numerator is the difference you have written in your question. To calculate percentage error just multiply relative error by 100.