# Thread: Simplification sine and cosine

1. ## Simplification sine and cosine

I've been given a question for an assignment due today and all it says is

Simplify:

a) Sin(n*Pi)
b) Cos(n*Pi)

Its a computer entered assignment, so i worked out that the answer to part a) is 0, I cant work out b) though. If it helps the assignment topic is on odd/even fourier series. Plz help

2. Originally Posted by martinr
I've been given a question for an assignment due today and all it says is

Simplify:

a) Sin(n*Pi)
b) Cos(n*Pi)

Its a computer entered assignment, so i worked out that the answer to part a) is 0, I cant work out b) though. If it helps the assignment topic is on odd/even fourier series. Plz help
$\displaystyle cos(0) = 1$

$\displaystyle cos(\pi) = -1$

$\displaystyle cos(2\pi) = 1$

$\displaystyle cos(3\pi) = -1$

See the pattern?

-Dan

3. Originally Posted by martinr
I've been given a question for an assignment due today and all it says is

Simplify:

a) Sin(n*Pi)
b) Cos(n*Pi)

Its a computer entered assignment, so i worked out that the answer to part a) is 0, I cant work out b) though. If it helps the assignment topic is on odd/even fourier series. Plz help

Remember what n stands for n is a natural number i.e 1,2,3,...

try a few

$\displaystyle \cos(1 \cdot \pi)=-1$

$\displaystyle \cos(2 \cdot \pi)=1$

$\displaystyle \cos(3 \cdot \pi)=-1$

so the pattern is $\displaystyle \cos(n\pi)=(-1)^n$