Question

How would one determine the percent uncertainty in theta and in sin of theta for the following:

1) theta = 15.0 degrees +/- 0.5 degrees
2) theta = 75.0 degrees +/- 0.5 degrees

I'm not sure whether I divide or use some kind of formula.

Answer 1

f(θ) = sin(θ)
f'(θ) = cos(θ)
For θ = 15°
d(cos(θ))
= ±cos(θ) dθ
= ±cos(15°) (0.5°)
= ±0.9659*(0.5*π/180)
= ±0.00843

Problem #2 can be calculated similarly.

Answer 2

I don't see "percentage uncertainty" in this answer. It looks to be just the uncertainty.