# Trigonometry/Power Series for Cosine and Sine

Applying Maclaurin's theorem to the cosine and sine functions for angle x (in radians), 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