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Power series for the cosine
The cosine can be expressed as a power series
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 formula only contains even numbers, so there is the symmetry
Example 1
You can see that cos (0) = 1, because