What is $\cos(k \pi)$? I want to ask question for which I have been finding answer for.
Please could anyone explain me why $\cos(k \pi) = (-1)^k$ and also explain me same for $\sin(k \pi)$?

I will do it the right way : 

This is a circle of radius $1$ unit. We complete the rectangle as shown and define $\sin$ and $\cos$ to be algebraic length on the respective axes as shown. Note that algebraic distance means that it can be negative also.
Now put that $\theta=\pi$
I hope you know the definition of angle. Clearly, $x-\text{coordinate}=-1$ Hence $cos\pi=-1$. What if it is $2\pi$? This time it is on positive side and it is $-1$. You can generalize it by using odd $k$ for former and even $k$ for latter.
