Values at 30, 45 and 60 Degrees — Cheat sheet

All six, at all three angles

Degrees	$30^\circ$	$45^\circ$	$60^\circ$
Radians	$\dfrac{\pi}{6}$	$\dfrac{\pi}{4}$	$\dfrac{\pi}{3}$

Half a turn is $\pi = 180^\circ$ .

Triangle	From	Sides
30-60-90	half an equilateral triangle of side $2x$	$x$ , $x\sqrt{3}$ , $2x$
45-45-90	a square of side $x$ cut along its diagonal	$x$ , $x$ , $x\sqrt{2}$

The $x$ cancels in every ratio. That is why the size of the triangle never matters.

Pattern	Why
The $30^\circ$ and $60^\circ$ columns are each other reversed	the two angles add to $90^\circ$
$\sin 45^\circ = \cos 45^\circ$	that triangle is isosceles
$\dfrac{1}{\sqrt{3}}$ is also written $\dfrac{\sqrt{3}}{3}$	some books clear the root from the bottom
Learn the radians too	calculus never asks in degrees