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