Find an angle's exact coordinates
Locate the angle on the chart, then read the point directly off the circle. The first number is the x-coordinate and the second is the y-coordinate.
COMPLETE VISUAL REFERENCE
Unit Circle Chart
A complete, labeled unit circle chart with all 16 standard angles — degrees, radians, exact coordinates, and sine, cosine, and tangent values in one printable diagram.
Vector-based, so it stays sharp at any zoom level. Free to print and share for classroom use.
DEGREES · RADIANS · EXACT VALUES
The Complete Unit Circle Chart
This chart shows all 16 standard angles from 0° to 330°, each labeled three ways: its degree measure, its radian measure, and its exact (x, y) coordinates.
Angles are measured counterclockwise from the positive x-axis. The x-coordinate of any point on the circle is cos θ, and the y-coordinate is sin θ — which is why the chart doubles as a trig values table.
Every value on this chart is exact, not rounded. You will see √2/2 rather than 0.707, because that is the form your textbook and your exam expect.
Start at 0° on the positive x-axis and move counterclockwise. Each label keeps the degree, radian, and coordinate forms together so the three representations can be read as one fact.
STRAIGHT-LINE REFERENCE
All 16 Angles: Degrees, Radians, Coordinates, and Values
If the diagram is hard to read on your screen, or you need the numbers in a straight line for a worksheet, here is the same information as a table.
| Degrees | Radians | Coordinates | sin θ | cos θ | tan θ |
|---|---|---|---|---|---|
| 0° | 0 | (1, 0) | 0 | 1 | 0 |
| 30° | π/6 | (√3/2, 1/2) | 1/2 | √3/2 | √3/3 |
| 45° | π/4 | (√2/2, √2/2) | √2/2 | √2/2 | 1 |
| 60° | π/3 | (1/2, √3/2) | √3/2 | 1/2 | √3 |
| 90° | π/2 | (0, 1) | 1 | 0 | undefined |
| 120° | 2π/3 | (−1/2, √3/2) | √3/2 | −1/2 | −√3 |
| 135° | 3π/4 | (−√2/2, √2/2) | √2/2 | −√2/2 | −1 |
| 150° | 5π/6 | (−√3/2, 1/2) | 1/2 | −√3/2 | −√3/3 |
| 180° | π | (−1, 0) | 0 | −1 | 0 |
| 210° | 7π/6 | (−√3/2, −1/2) | −1/2 | −√3/2 | √3/3 |
| 225° | 5π/4 | (−√2/2, −√2/2) | −√2/2 | −√2/2 | 1 |
| 240° | 4π/3 | (−1/2, −√3/2) | −√3/2 | −1/2 | √3 |
| 270° | 3π/2 | (0, −1) | −1 | 0 | undefined |
| 300° | 5π/3 | (1/2, −√3/2) | −√3/2 | 1/2 | −√3 |
| 315° | 7π/4 | (√2/2, −√2/2) | −√2/2 | √2/2 | −1 |
| 330° | 11π/6 | (√3/2, −1/2) | −1/2 | √3/2 | −√3/3 |
Tangent is undefined at 90° and 270°, where cos θ = 0 and the ratio y ÷ x has no value.
Use the diagram when position matters and the table when you need to compare rows. Both show one full turn from 0° up to, but not including, 360°; the 360° point lands back at (1, 0), so it repeats the first row rather than creating a seventeenth standard point.
READ THE SIGNS
Quadrant Signs: How to Read the Negative Values
The unit circle is divided into four quadrants, and the signs of sine and cosine flip in each one.
In Quadrant I both coordinates are positive. In Quadrant II, x is negative and y is positive. In Quadrant III both are negative. In Quadrant IV, x is positive and y is negative.
Read it as cos θ = x, sin θ = y, and tan θ = y ÷ x. Their reciprocals follow the same signs: sec θ = 1/x, csc θ = 1/y, and cot θ = x/y.
Quadrant I(+, +)All six functions positive
Quadrant II(−, +)Positive: sin, csc · Negative: cos, sec, tan, cot
Quadrant III(−, −)Positive: tan, cot · Negative: sin, csc, cos, sec
Quadrant IV(+, −)Positive: cos, sec · Negative: sin, csc, tan, cot
The axes are the boundary cases. At 0° and 180°, the y-coordinate is zero; at 90° and 270°, the x-coordinate is zero. Reading the coordinate before the trig function prevents sign errors and also makes the two undefined tangent values easy to identify.
THREE QUICK USES
How to Use the Unit Circle Chart
Use the chart as a lookup tool first, then cover the labels and try to reconstruct the same information from the angle position alone.
Check a trig value without a calculator
For any standard angle, sine is y and cosine is x. Then tan = y/x, sec = 1/x, csc = 1/y, and cot = x/y.
Convert between degrees and radians
The degree measure is written on the outer ring and the radian measure on the inner ring, so you can read a conversion straight off the chart. To convert by hand, multiply degrees by π/180.
For example, locate 150° in Quadrant II. The same label shows 5π/6 and the point (−√3/2, 1/2), so cos 150° = −√3/2, sin 150° = 1/2, and tan 150° = −√3/3 without switching between separate references.
KEEP A COPY
Print or Download the Chart
The chart is sized to fit a standard letter or A4 sheet without cutting off any labels. Print it for a notebook, a binder, or a classroom wall.
For the blank version you can fill in yourself, open the blank unit circle.
The PDF includes the complete labeled diagram and the exact-values table on a single landscape page. It is useful as a worksheet reference, a handout beside a trigonometry assignment, or a clean unit circle chart PDF to keep offline.
COMMON QUESTIONS
Unit Circle Chart FAQ
What is a unit circle chart?
A unit circle chart is a labeled diagram of a circle with radius 1 centered at the origin. It connects each standard angle to its degree measure, radian measure, exact coordinates, and sine, cosine, and tangent values.
What are the 16 angles on a unit circle chart?
The 16 standard angles are 0°, 30°, 45°, 60°, 90°, 120°, 135°, 150°, 180°, 210°, 225°, 240°, 270°, 300°, 315°, and 330°. The point at 360° repeats the point at 0°.
Is the unit circle chart in degrees or radians?
This unit circle chart shows both. Degrees appear with the degree symbol, and the equivalent radian measures appear in terms of pi so you can convert between the two systems directly.
Where is tangent undefined on the unit circle chart?
Tangent is undefined at 90° (π/2) and 270° (3π/2). At those two points the x-coordinate, which equals cosine, is zero, so the ratio sine divided by cosine has a zero denominator.
Can I print the unit circle chart?
Yes. Use the print button for a clean chart and values table, or download the prepared PDF. The diagram is vector-based, so the labels and lines remain sharp when printed or enlarged.
Want to test yourself instead of reading the chart? Play the unit circle game.
Looking for the memory tricks behind these values? See the unit circle cheat sheet.
Need a printable practice copy with the labels removed? Open the blank unit circle.