I have some trouble with taylor series,but it all comes down to basic trig questions,for example

1)for the taylor series of f(x)=sinx,the textbook states that f^{(}^{n)}(x)=sin(x+nπ/2)

Is it because for every n+1 it just goes form cosx to -sinx and from -sinx to -cosx and so on?

2)Find the first three terms of the Taylor series for the function f(x)=sin(-x^{2}+πx+π/2).When I try to solve this one I get cos(-1+3π/2) among others,for example f'(1)=cos(3π/2 -1)(π-2).How do I approach that?

EDIT: Is it f'(1)=(cos(π/2-1))(π-2)=(sin(-1))(π-2) ?

(my mistake,this should've been in pre calculus forum I guess)