# MacLaurin series of Trigonometric function

The MacLaulin series (Taylor series at ) representation of a function is

## Cosine, cos *x*

The derivatives of the trigonometric function and their values at are:

We substitute this value of in the MacLaurin series:

## Sine, sin *x*

The derivatives of the trigonometric function and their values at are:

We substitute this value of in the MacLaurin series: