What is a Unit Circle |

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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?

Free What is a Unit Circle Calculator - 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?

Unit Circle Origin = (0,0)
radius = 1
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?

circlethe set of all points in the plane that are a fixed distance from a fixed pointequationa statement declaring two mathematical expressions are equaloriginOn a two digit coordinate plane, the point (0, 0), where the x-axis and y-axis cross.pointan exact location in the space, and has no length, width, or thicknessradiusDistance from the center of a circle to the edge
C/2πtrigonometryTrigonometry 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 measureunit circleA circle centered at the origin (0, 0) with a radius of 1
x2 + y2 = 1