[Math] Uncertainty/error calculation (product of number and trig)

Question

I understand how to multiply two numbers with errors together.
However, I am unsure how to do a problem when there is trig involved:

$$ (100 \pm 10) \cdot \sin(30 \pm 1) $$

What are the steps I should take to solve it?

Answer 1

There is something called propagation of errors invented for your sort of problem: read about it here. (That web page has a chart with a formula for the $sin$ function.) It is more-or-less the cousin of the delta method, but more aimed at practical measurement problems instead of proving theorems.