# Thread: Expanding Sine cardinal with Taylor Series

1. ## Expanding Sine cardinal with Taylor Series

Hi,
I am trying to expand the sine cardinal (sin(x)/x) using the Taylor series around x=PI. Then I need to show that when x is near PI, the result is approx 0.0525.

My problem is when working out the derivatives. f(0)=1 but f'(0) leads to cos(0)/0 which is infinity.

2. ## Re: Expanding Sine cardinal with Taylor Series

hmm, a few questions for you first.
f = sin(x) / x
then
1. f(pi) = 0 surely? What do you mean you want to show its 0.0525?
2. you are expanding around pi, why do you need f(0)?
3. f'(0) = f'(x) at 0, and have you worked out f'(x)?