# Trigonometry/Power Series for Cosine and Sine

< Trigonometry(Redirected from Trigonometry/Power Series for Cosine)

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Applying Maclaurin's theorem to the cosine and sine functions, we get

For both series, the ratio of the nth to the (n-1)th term tends to zero for all *x*. Thus both series are absolutely convergent for all *x*.

Many properties of the cosine and sine functions can easily be derived from these expansions, such as