Use the definition of taylor series to find the taylor series (centered at c. for the function. f(x) = cos x, c = π 4

Cos(x) is infinitely differentiable, can be expanded using Taylor's series.
The series about c can be expressed as

Substituting cos(x), c= π /4,we have

and since





we can simplify the expansion to 

Note that the sign pattern is  - - + + - - + + - - ..... following the sign pattern of the derivatives of cos(x).

They are somewhat similar