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Unit circle

This original textbook reading covers part of the AP topic. Follow the AP course outline for complete topic instruction and practice.

Unit circle

Important values described below

$\begin{matrix} angle(θ) & \sin θ & \cos θ & \tan θ \\ \frac{π}{6} & \frac{1}{2} & \frac{\sqrt{3}}{2} & \frac{\sqrt{3}}{3} \\ \frac{π}{4} & \frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2} & 1 \\ \frac{π}{3} & \frac{\sqrt{3}}{2} & \frac{1}{2} & \sqrt{3} \end{matrix}$

The unit circle is a circle with a radius of 1, which helps us understand the values of trigonometric ratios (sin x, cos x, tan x) because it simplifies the hypotenuse to 1.

Related Glossary Terms

Sinusoidal function

Index

How to Use - How to Use

Chapter 1 - An Overview of Trigonometry

Chapter 4 - FFR - Implicit Differentiation

Chapter 5 - Inverse Functions

Chapter 6 - Maximinima

Glossary and deeper reading · 1 refreshers

These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.

Unit circle
The unit circle is the circle of radius 1 centered at the origin. At angle θ measured from the positive horizontal axis, its point has coordinates (cos θ, sin θ). For example, θ=π/2 gives the point (0,1), so cosine is 0 and sine is 1. The circle also helps track signs and periodic behavior of trigonometric functions.

Unit circle

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