What is the minimal degree Taylor polynomial about x 0 that

What is the minimal degree Taylor polynomial about x = 0| that you need to calculate sin(1)| to 3 decimal places? To 6 decimal places?

Solution

The Taylor polynomial about x = 0 for

sin x=
x - x^3/3! + x^5/5! - x^7/7! + ...

I assume you mean 1 radian.
sin 1 = approx. 0.84147 or 0.841 to the nearest 3 decimal places