4
$\begingroup$

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?

$\endgroup$
6
$\begingroup$

There are an infinity of values... But you mean the common values $\pi$, $\pi/6$, $\pi/4$, $\pi/3$, $\pi/2$. It is easy to memorize them as follows: $$ \begin{array}{c|c|c} \theta& \sin\theta & \cos\theta \\ \ \\ \hline 0 & \frac{\sqrt0}2&\frac{\sqrt4}2\\ \hline\frac\pi6 & \frac{\sqrt1}2&\frac{\sqrt3}2\\ \hline\frac\pi4 & \frac{\sqrt2}2&\frac{\sqrt2}2\\ \hline\frac\pi3 & \frac{\sqrt3}2&\frac{\sqrt1}2\\ \hline\frac\pi2 & \frac{\sqrt4}2&\frac{\sqrt0}2\\ \end{array} $$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.