Given an complex number $z=a+bi$, we could find the polar form. For example $z=1+\sqrt{3}i$ has radius $2$ and $\arg z=\frac{\pi}{3}$.
My question is: Do I have to memorize all the possible sin and cosine values for every possible argument $\theta$? How can I know without a calculator that $\cos \theta$ = 1/2 and $\sin\theta=\frac{\sqrt{3}}{2}$ satisfies $ \theta = \frac{\pi}{3}$ ? How can I memorize this values efficiently?