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MacLaurin series of Trigonometric function

The MacLaulin series (Taylor series at x=0) representation of a function f(x) is
Definition of MacLaurin series

Cosine, cos x

The derivatives of the trigonometric function cos x and their values at x=0 are:

Derivatives of cos x

We substitute this value of f^{(n)}(0) in the MacLaurin series:

Maclaurin series of cos

Sine, sin x

The derivatives of the trigonometric function sin x and their values at x=0 are:

Derivatives of sin

We substitute this value of f^{(n)}(0) in the MacLaurin series:

Maclaurin series of sin

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