evaluate cos 12*pi

Answer 1

In radian measure that last pair of equations read as

sin ( theta + 2 k pi ) = sin ( theta )

In this case:

2 k pi = 12 pi Divide both sides with 2 pi

k = 6

sin ( theta + 2 k pi ) = sin ( 0 + 12 pi )

This mean theta = 0

sin ( 0 + 12 pi ) =

sin ( 0 ) = 0

Starting from zero, this means rotating through pi or180º 12 times counter-clockwise which ends at zero.

So:

sin ( 12pi ) = 0