Question

Values of following....I'm doing fourier series btw..
Sin(n*pi),cos(n*pi),sin(2n*pi),cos(2n*pi),sin(2*pi),cos(2*pi)..

Answer 1

so,
if you have the unit circle in mind,
you can answer these easily :)
https://en.wikipedia.org/wiki/Unit_circle#/media/File:Unit_circle_angles_color.svg

\( n\pi \) means 180 degrees rotation from 0, for each values of n.
so, 0,180,360,540,...

\( 2n\pi \) means 360 degrees rotation from 0, for each values of n.
so, 0,360,720,...

for sin, we see y-co-ordinate,
sin 0 = 0,
sin 180 = 0,
so on,
so
\(\sin n\pi =0 \)
always.

similarly, \(\sin 2\pi = 0 \\
\sin 2n\pi = 0\)

Now for cos, we see x co-ordinate,
cos 0 = 1,
cos pi = -1
cos 2pi = 1
so on.

\(\cos 2n\pi = 1\)
\(\cos 2\pi = 1\)

\(\cos n \pi = +1 \) for n = even,
\(\cos n \pi = -1 \) for n = odd,
which we write as
\(\cos n\pi = (-1)^n\)

simply because (-1)^n = +1 for n = even and -1 for n = odd.

let me know if any doubts :)

(n*pi)s and (2n*pi)s are easy, more trickier are (n*pi/2')s :P

Answer 2

@simran2590

Answer 3

Thanks..can you also explain sin and cos values for n*pi?

Answer 4

did above...

\(\sin n\pi = 0 \)
\(\cos n\pi = (-1)^n\)

what exactly are you looking in the explanation?

Answer 5

Sorry I meant n*pi/2