How to memorize the points on the unit circle

To memorize the points on the unit circle, remember that the unit circle has a radius of 1 and is centered at the origin (0,0). The key angles in radians are

txt1

txt1

txt1

$, $\frac{\pi}{6}$, $\frac{\pi}{4}$, $\frac{\pi}{3}$, $\frac{\pi}{2}$, and so on, up to $2\pi$. Each angle corresponds to coordinates (cosine, sine):

$\begin{aligned} (0,1) & \quad \text{at} \quad 0 \\ (\frac{1}{2}, \frac{\sqrt{3}}{2}) & \quad \text{at} \quad \frac{\pi}{6} \\ (\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}) & \quad \text{at} \quad \frac{\pi}{4} \\ (\frac{\sqrt{3}}{2}, \frac{1}{2}) & \quad \text{at} \quad \frac{\pi}{3} \\ (1,0) & \quad \text{at} \quad \frac{\pi}{2} \end{aligned}$

To recall the unit circle, focus on the main angles in radians:

txt2

txt2

txt2

$, $frac{pi}{6}$, $frac{pi}{4}$, $frac{pi}{3}$, $frac{pi}{2}$. At each angle, the coordinates are calculated as (cosine, sine). For instance:

$ ext{at} frac{pi}{6}, cos(frac{pi}{6}) = frac{sqrt{3}}{2}, sin(frac{pi}{6}) = frac{1}{2} $

$ ext{Coordinates}: (frac{sqrt{3}}{2}, frac{1}{2}) $

Memorize the unit circle by remembering key angles and their coordinates (cosine, sine):

$ frac{pi}{6}
ightarrow (frac{sqrt{3}}{2}, frac{1}{2}) $

$ frac{pi}{4}
ightarrow (frac{sqrt{2}}{2}, frac{sqrt{2}}{2}) $

Start Using PopAi Today