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in fourier series cos(npi) is (-1)^n and sin(npi)=0, what is cos(npi/2) and sin(npi/2)? and when the answer is 0 when n is odd i change n into 2n, while if answer is 0 when n is even i change n into 2n-1. do i apply the same thing for npi/2?

Mathematics
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im always stucked here when im doing the cosine and sine series in the PDE, especially when its stepfunction with pi as interval.
\[\cos(\pi/2n) = \begin{cases} (-1)^{n/2} &\;\;\;\;\;\;\text{if }n\text{ is even}\\ 0 &\;\;\;\;\;\;\text{if }n\text{ is odd} \end{cases}\]\[\sin(\pi/2n) = \begin{cases} 0 &\;\text{if }n\text{ is even}\\ (-1)^{(n-1)/2} &\;\text{if }n\text{ is odd} \end{cases}\]
oh. so if i want n to represent for all n, change n into 2n if n is odd gives 0, and change n into 2n-1 if n is even gives 0?

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