Cosine
The power series for the cosine is
Explanation
As the cosine can be differentiated continuously, you get
The point x = 0 gives cos (0) = 1 and sin (0) = 0 so
We substitute this in the Taylor series and find
so
Symmetry
The power series only contains even exponents, so there is the symmetry
what you can clearly see in the graphic
Example 1
You can see that cos (0) = 1, because