A Trick to Memorizing Trig Special Angle Values Table

[benorin]

In calculus classes when you are asked to evaluate a trig function at a specific angle, it’s 99.9% of the time at one of the so-called special angles we use in our chart. Since you are likely to have learned degrees first I’ll include degree angles in the first chart, but after that, it’s going to be radian only.
Begin by setting up the table on scratch paper as follows:
$$\begin{array}{ l| |c|c|c|c|c } \theta & 0 = 0º & \tfrac{\pi}{6} = 30º & \tfrac{\pi}{4}=45º & \tfrac{\pi}{3}=60º & \tfrac{\pi}{2}=90º \\ \hline\hline \sin\theta &   &   &  &   &    \\ \hline \cos\theta &   &    &    &    &    \\ \hline \tan\theta &    &    &    &   &    \\ \hline \end{array} $$
Then remember $\sin\theta$ starts at zero, fill in the pattern
$$\begin{array}{ l| |c|c|c|c|c } \theta & 0 & \tfrac{\pi}{6} & \tfrac{\pi}{4} & \tfrac{\pi}{3} & \tfrac{\pi}{2} \\ \hline\hline\sin\theta & \tfrac{\sqrt{0}}{2} & \tfrac{\sqrt{1}}{2} & \tfrac{\sqrt{2}}{2} & \tfrac{\sqrt{3}}{2} & \tfrac{\sqrt{4}}{2} \\...

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[neilparker62]

I think I'll make this compulsory reading for my Maths students!

 

[Wrichik Basu]

In our junior classes, we learned it in a similar way:

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$\theta~\rightarrow$​	0° = 0​	30° = $\dfrac{\pi}{6}$​	45° = $\dfrac{\pi}{4}$​	60° = $\dfrac{\pi}{3}$​	90° = $\dfrac{\pi}{2}$​
$\sin \theta$​	$\sqrt{\dfrac{0}{4}}$​	$\sqrt{\dfrac{1}{4}}$​	$\sqrt{\dfrac{2}{4}}$​	$\sqrt{\dfrac{3}{4}}$​	$\sqrt{\dfrac{4}{4}}$​
$\cos \theta$​	$\sqrt{\dfrac{4}{4}}$​	$\sqrt{\dfrac{3}{4}}$​	$\sqrt{\dfrac{2}{4}}$​	$\sqrt{\dfrac{1}{4}}$​	$\sqrt{\dfrac{0}{4}}$​
$\tan \theta$​	$\sqrt{\dfrac{0}{4 - 0}}$​	$\sqrt{\dfrac{1}{4 - 1}}$​	$\sqrt{\dfrac{2}{4 - 2}}$​	$\sqrt{\dfrac{3}{4 - 3}}$​	$\sqrt{\dfrac{4}{4 - 4}}$​

 

[symbolipoint]

"Trick"? The very basics of triangle Geometry and the Pythagorean Theorem, and The UNIT CIRCLE.

Easily enough done, drawing a Unit Circle and judging Sines and Cosines, and whichever other of the functions to derive what you need. Degree measures 30, 45, 60, 0, and 90, and 180 are the easy ones and are commonly used "Reference" angles.