 # What is a Unit Circle

## Unit Circle Definition:

A circle centered at the origin (0, 0)
It has radius of 1 unit.

Unit circle equation:
x2 + y2 = 1 ## Circle Equation:

Center at (a, b) and radius length r
(x - a)2 + (y - b)2 = r2

## Unit Circle Conversion:

(x, y) with a center (0, 0) and radius = 1
(x - 0)2 + (y - 0)2 = 12

x2 + y2 = 1

## Trigonometry Uses:

With radius = 1, we can do this:
trignometry measurements like sin, cos, and tan

## sin measurement for θ on the unit circle:

 sin(θ)  = Opposite Side of θ Hypotenuse

 sin(θ)  = y 1

sin(θ) = y

## cos measurement for θ on the unit circle:

 cos(θ)  = Adjacent Side of θ Hypotenuse

 sin(θ)  = x 1

cos(θ) = x

## tan measurement for θ on the unit circle:

 tan(θ)  = Opposite Side Adjacent Side

 tan(θ)  = y x

Or, tan(θ) is also known as
 tan(θ)  = sin(θ) cos(θ)

## Trig Identity:

Recall above that x2 + y2 = 1

Since x = cos(θ) and y = sin(θ):
cos2(θ) + sin2(θ) = 1

### How does the What is a Unit Circle Calculator work?

This lesson walks you through what a unit circle is and how to use it

### What 3 formulas are used for the What is a Unit Circle Calculator?

1. Unit Circle Origin = (0,0)
3. x2 + y2 = 1

For more math formulas, check out our Formula Dossier

### What 7 concepts are covered in the What is a Unit Circle Calculator?

circle
the set of all points in the plane that are a fixed distance from a fixed point
equation
a statement declaring two mathematical expressions are equal
origin
On a two digit coordinate plane, the point (0, 0), where the x-axis and y-axis cross.
point
an exact location in the space, and has no length, width, or thickness
Distance from the center of a circle to the edge
C/2π
trigonometry
Trigonometry studies relationships between side lengths and angles of triangles. The word trigonometry comes from the Greek word trigonon which means triangle and metron which means measure
unit circle
A circle centered at the origin (0, 0) with a radius of 1
x2 + y2 = 1