Error analysis?

Question

IMA = 1/sin(a)

I have a at 20 degree + or minus 0.5 degree.

How do I calculate the uncertainty of IMA ?

Answer 1

let IMA = IMA(a) = 1/sin(a)

Then a varaition of a yields

d IMA(a)/da = -cos(a)/sin(a)^2 or expressed as variation

D IMA = -cos(a)/(sin(a))^2 Da where Da is a small change in a


Now convert your measurements to radians. Da = 0.5 deg = 8.7 milliradians, a = 20 deg = 349.1 milliradians

Then D IMA = -cos(a)/(sin(a))^2 *8.7e-3 =-/+0.0701

Answer 2

20 degree + 0.5 degree = 20.5 degree
20 degree - 0.5 degree = 19.5 degree
therefore the IMA is equal to the 19.5 degree to 20.5 degree