use Maclaurin series for sin(x) to compute sin 3 degrees

Question

how do I know which n to use, I see a lot of people going up to sin^7/7! but why 7?

Answer 1

The more terms are used in the computation (approximation), the more accurate the computed value is.

 

You can get a feel for this by taking the radian number corresponding to 3 degrees and raising it to the 7th; even before dividing by 7! you see that this term has many zeros after the decimal point until finally a significant figure occurs.