In the Fourier series, what are all the ways we can express:
- $\displaystyle\sin\left(\frac{n\cdot\pi}2\right)$
- $\displaystyle\cos(n\cdot\pi)$
I know we can express
- as $(-1)^{(n+1)}$, and
- as $(-1)^n$.
What other forms are there? I have seen a question where there has been a $\cos(n\cdot\pi)$, which when put back in the series had been changed to $\cos((2m+1)x)$. Could somebody explain this please?