Unit Circle Trigonometry

Vocabulary flashcards covering key angles in degrees, radians, and coordinate points on the unit circle.

Unit Circle Diagram

A circle with radius $1$ centered at the origin $(0,0)$ used in trigonometry to define functions of angles in terms of $(x, y) = (\cos(\theta), \sin(\theta))$.

Unit Circle Coordinates at $0^\circ$ ($0\text{ rad}$)

$$(1, 0)$$

Unit Circle Coordinates at $30^\circ$ ($\frac{\pi}{6}\text{ rad}$)

$$\left(\frac{\sqrt{3}}{2}, \frac{1}{2}\right)$$

Unit Circle Coordinates at $45^\circ$ ($\frac{\pi}{4}\text{ rad}$)

$$\left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)$$

Unit Circle Coordinates at $60^\circ$ ($\frac{\pi}{3}\text{ rad}$)

$$\left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right)$$

Unit Circle Coordinates at $90^\circ$ ($\frac{\pi}{2}\text{ rad}$)

$$(0, 1)$$

Unit Circle Coordinates at $120^\circ$ ($\frac{2\pi}{3}\text{ rad}$)

$$\left(-\frac{1}{2}, \frac{\sqrt{3}}{2}\right)$$

Unit Circle Coordinates at $135^\circ$ ($\frac{3\pi}{4}\text{ rad}$)

$$\left(-\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)$$

Unit Circle Coordinates at $150^\circ$ ($\frac{5\pi}{6}\text{ rad}$)

$$\left(-\frac{\sqrt{3}}{2}, \frac{1}{2}\right)$$

Unit Circle Coordinates at $180^\circ$ ($\pi\text{ rad}$)

$$(-1, 0)$$

Unit Circle Coordinates at $210^\circ$ ($\frac{7\pi}{6}\text{ rad}$)

$$\left(-\frac{\sqrt{3}}{2}, -\frac{1}{2}\right)$$

Unit Circle Coordinates at $225^\circ$ ($\frac{5\pi}{4}\text{ rad}$)

$$\left(-\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}\right)$$

Unit Circle Coordinates at $240^\circ$ ($\frac{4\pi}{3}\text{ rad}$)

$$\left(-\frac{1}{2}, -\frac{\sqrt{3}}{2}\right)$$

Unit Circle Coordinates at $270^\circ$ ($\frac{3\pi}{2}\text{ rad}$)

$$(0, -1)$$

Unit Circle Coordinates at $300^\circ$ ($\frac{5\pi}{3}\text{ rad}$)

$$\left(\frac{1}{2}, -\frac{\sqrt{3}}{2}\right)$$

Unit Circle Coordinates at $315^\circ$ ($\frac{7\pi}{4}\text{ rad}$)

$$\left(\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}\right)$$

Unit Circle Coordinates at $330^\circ$ ($\frac{11\pi}{6}\text{ rad}$)

$$\left(\frac{\sqrt{3}}{2}, -\frac{1}{2}\right)$$