Find the Taylor's formula for the given function f at a=0. Find both the Taylor polynomial of the indicated degree n and the remainder term

f(x)=sinx n=4

f(x)=cosx n=4

I thought the Taylor formula and the remainder term for f(x)=cosx n=4, was

1 - ((x^2)/2!) + ((x^4)/4!) - ((x^6)/6!) + ((x^8)/8!) - ((sinz)(x^5))/5!

However, the book tells me that the answer is 1 - ((x^2)/2!) + ((x^4)/4!) - ((sinz)(x^5))/5! . What am I doing wrong here and how should i solve f(x)=sinx n=4?