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

Accepted Solution

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).