Trigonometry visual reference

Unit Circle Chart: Degrees, Radians & Trig Values

The unit circle turns an angle into a point: the x-coordinate is cosine and the y-coordinate is sine. This chart groups the standard angles by quadrant so signs and reference-angle patterns stay visible.

Download full PDFDownload full SVGDownload chart PNG
Unit circle chart labeled with standard angles in degrees and radians and exact cosine sine coordinate pairs in all four quadrants
Open the chart for a full-size, printable version.
How to read it

Use the chart as a decision tool.

A complete unit circle chart with degrees, radians, ordered pairs, and exact sine and cosine values, plus a blank printable practice circle. Read the label first, identify the matching structure in your problem, then confirm that any stated conditions apply before substituting values.

01

How the coordinates work

Every point on the unit circle has radius 1.

Coordinate rule

P(θ)=(cos⁡θ,sin⁡θ)\displaystyle P(\theta)=(\cos\theta,\sin\theta)

Pythagorean identity

cos⁡2θ+sin⁡2θ=1\displaystyle \cos^2\theta+\sin^2\theta=1
02

Quadrant signs

Use the reference angle for magnitude and the quadrant for signs.

Quadrant I

cos⁡θ>0, sin⁡θ>0\displaystyle \cos\theta>0,\ \sin\theta>0

Quadrant II

cos⁡θ<0, sin⁡θ>0\displaystyle \cos\theta<0,\ \sin\theta>0

Quadrant III

cos⁡θ<0, sin⁡θ<0\displaystyle \cos\theta<0,\ \sin\theta<0

Quadrant IV

cos⁡θ>0, sin⁡θ<0\displaystyle \cos\theta>0,\ \sin\theta<0
How to remember it

Memorize one quadrant, then use signs

  1. 1Learn 0°, 30°, 45°, 60°, and 90° first.
  2. 2Cosine is the x-coordinate; sine is the y-coordinate.
  3. 3Reflect the first-quadrant values and apply the quadrant sign pattern: all, sine, tangent, cosine.
Printable practice

Blank unit-circle practice chart

Print the unlabeled circle and fill in degrees, radians, coordinates, sine, and cosine from memory.

Download practice SVGDownload practice PNG
Blank printable unit circle with axes, quadrant labels, and empty angle markers for student practice
Keep learning