Uncertain about this uncertainty problem!?

[Guest SNJERIN]

Which method of those two is appropriate in determining the uncertainty of trigonometric ratios 

[Vioh]

Which method of those two is appropriate in determining the uncertainty of trigonometric ratios 

 

First, I think that your question doesn't have much to do with the uncertainty of the trigonometric function. What you are really wondering is whether to use the max/min method or the trick with percentage error to calculate the uncertainty of a number division. Well, in the case, both methods that you described above are correct. In fact, that's usually the case if you're working with statistics and uncertainties. There's no ONE way of computing the uncertainty, but many many ways, each is good for under some certain occasions. The second method that you mentioned should be pretty straight forward to understand. For the first method, you can take a look here for a quick derivation.

 

Now, despite the fact that both are valid, the first method is more preferred in most cases. The reason is because it gives a lower range for the uncertainty which means that it only takes into account the part where most data are statistically located, which is what we try to aim in statistics under most cases. Besides, the formula for the first method is also much simpler and easier to use!