Trig circle: the 4 values to memorize (0°, 30°, 45°, 60°, 90°)

The table to memorize

Angle	0°	30°	45°	60°	90°
$\cos$	$1$	$\dfrac{\sqrt{3}}{2}$	$\dfrac{\sqrt{2}}{2}$	$\dfrac{1}{2}$	$0$
$\sin$	$0$	$\dfrac{1}{2}$	$\dfrac{\sqrt{2}}{2}$	$\dfrac{\sqrt{3}}{2}$	$1$

The raised-hand trick

Number your fingers 0 to 4 (thumb = 0, index = 1, middle = 2, ring = 3, pinky = 4). For the corresponding angle:

$\cos(\text{angle}) = \dfrac{\sqrt{\text{fingers on the left}}}{2}, \quad \sin(\text{angle}) = \dfrac{\sqrt{\text{fingers on the right}}}{2}$

Example for $60°$ (middle finger, 3rd finger): 3 fingers on the left, 1 on the right → $\cos(60°) = \sqrt{1}/2 = 1/2$, $\sin(60°) = \sqrt{3}/2$.

The symmetry shortcut

$\cos$ and $\sin$ are symmetric in the table (mirror). Learn one, get the other by reading backwards.

In radians

Convert: $30° = \pi/6$, $45° = \pi/4$, $60° = \pi/3$, $90° = \pi/2$. Same values apply.

The unavoidable identity

$\cos^2(\theta) + \sin^2(\theta) = 1$

Check at $\theta = 30°$: $(\sqrt{3}/2)^2 + (1/2)^2 = 3/4 + 1/4 = 1$ ✓.

?Your turn

What is cos(60°)?

A.√3/2B.1/2C.√2/2D.1

Check