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.

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

    Problem #2 can be calculated similarly.

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

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