How do you use Taylor series for #sin(x)# at #a = pi/3#?
Just plug values for
The Taylor series for
If you, for example, substitute
Using a calculator (in radian mode) gives the same approximation to 5 decimal places (actually, if you carry it out further, it's accurate to 10 decimal places).
To know how accurate you are guaranteed to be requires more theory (see especially Theorem 4 at the following link: http://www.stewartcalculus.com/data/CALCULUS%20Early%20Transcendentals/upfiles/Formulas4RemainderTaylorSeries5ET.pdf )