Question

Find the Taylor series generated by f(x)=sin^2x at x=π /2


edit: I thought that we should be using π /2 as "a" in taylor series formula. but in the answer π /2 is positive.

Answer 1

ouch

Answer 2

First off, this should make sense that the answer is positive, since the square of a negative or positive number is always positive.

So what are you doing here? Are you taking the derivative of sin^2(x) and at each derivative evaluating it at π/2?

Answer 3

Before you even do that, it might help to rewrite \(\sin^2x=\dfrac{1}{2}-\dfrac{1}{2}\cos2x\) to avoid all that product/power rule.