Unit Circle, Argument, Cis, Polar Form

Let $\cos a= x, \sin a= y$.

Then $x^2+y^2=1$.

Ok, so we've found that each point on the unit circle can be expressed in the form $(\cos a, \sin a)$.

What about each point on the circle $x^2+y^2=4$?

Well, it's just the unit circle x2, so we conclude each point on that circle is just $(2 \cos a, 2 \sin a)$.

It's not hard to see that if $O=(0,0)$, point $P=(\cos a, \sin a)$ has a equal to the angle between $OP$ and the x-axis. (We just draw the right triangle).