## edr1c Group Title 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? one year ago one year ago

1. edr1c Group Title

im always stucked here when im doing the cosine and sine series in the PDE, especially when its stepfunction with pi as interval.

2. Herp_Derp Group Title

$\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}$

3. edr1c Group Title

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?