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**mathfied** for example, $\displaystyle cos(m\pi)$ = $\displaystyle (-1)^m$ because cos alternates between 1 and -1 every $\displaystyle m\pi$.

so how can you represent $\displaystyle cos(\frac{m\pi}{2})$ in power form?

this one is a bit confusing to me because when:

m=1, $\displaystyle cos(\frac{m\pi}{2})=cos(\frac{1\pi}{2})$= 0

m=2, $\displaystyle cos(\frac{m\pi}{2})=cos(\frac{2\pi}{2})$= -1

m=3, $\displaystyle cos(\frac{m\pi}{2})=cos(\frac{3\pi}{2})$= 0

m=4, $\displaystyle cos(\frac{m\pi}{2})=cos(\frac{4\pi}{2})$= 1