Finding Taylor polynomial

Question

Find the Taylor polynomial of degree n = 4 approximating the function f(x) = 11cos(x) for x near pi/2

Answer 1

The first 4 terms would be f(x) = -11(x - pi/2) + 11(x - pi/2)³/3! - 11(x - pi/2)⁵/5! + 11(x - pi/2)⁷/7!