Connect degrees & radians
A full turn is 360° or 2π radians. Multiply degrees by π/180, simplify the fraction, and connect that value to a position on the circle.
Practice radiansA LITTLE PRACTICE. A FULL CIRCLE.
Unit Circle Quiz
Connect the angles. Find the patterns. Make them stick.
Convert 150° to radians.
Convert the angle and give the exact value.
THE UNIT CIRCLEr = 1
Angles turn counterclockwise from the positive x-axis.
Quadrant signs
QII(−, +)
QI(+, +)
QIII(−, −)
QIV(+, −)
cos θ = x-coord · sin θ = y-coord · tan θ = y ÷ x
Select a point on the circle.
No timer. One first attempt per question. Hints are recorded separately.
POINT A
Use angles from 0° to less than 360° (0 to less than 2π). Each saved point has 3 items.
Filled ● Correct ✓ Needs work ! Blank ○
Open graded fill-in practice: degrees, radians, coordinates, or the full circle →
ROUND COMPLETE
A little closer to full circle.
These are first-attempt results from this round, not a grade or a measure of ability.
This round, by topic
Review every answer
Your mastery map
Color shows first-attempt accuracy from quiz practice saved in this browser.
● Solid ● Practicing ● Needs work ● No data
Weak spots from your practice history
Based on first-attempt quiz answers stored in this browser.
New to the unit circle? Learn the 30°–45°–60° pattern, the √n/2 shortcut, reference angles, and quadrant signs before you drill them. Learn the unit circle by pattern →
Already know the values? Switch from understanding to fluency with a 60-second sprint, a 2-minute sprint, or a full recall challenge. Take the unit circle speed test →
SEE THE CONNECTION
Explore every unit circle angle.
Choose any point to connect its position with radians, coordinates, sine, cosine, tangent, and quadrant signs.
Tap or click any standard angle. The ray, coordinate projections, and exact values update together.
SELECTED ANGLE
30° · π/6
Quadrant I · reference angle 30°
- Coordinates
- (√3/2, 1/2)
- cos θ = x
- √3/2
- sin θ = y
- 1/2
- tan θ = y ÷ x
- √3/3
Coordinates always read (cos θ, sin θ). The quadrant changes the signs; the reference angle keeps the magnitudes.
SMALL STEPS, STRONGER RECALL
Find your way around the circle.
The angle, the point, and the exact value tell the same story. Practice connecting them.
Get the coordinates right
The x-coordinate is cosine; the y-coordinate is sine. Learn the first-quadrant values, then use the quadrant to decide each sign.
Practice coordinatesSee the trig relationships
Sine and cosine come straight from the point. Tangent is y divided by x, and is undefined when x is zero, at 90° and 270°.
Practice trig valuesYOUR STUDY COMPANION
Unit circle reference.
Study the patterns here. When you’re ready, test your recall with the quiz.
Show all 16 angles and exact values
| Point | Degrees | Radians | cos θ / x | sin θ / y | tan θ |
|---|---|---|---|---|---|
| A | 0° | 0 | 1 | 0 | 0 |
| B | 30° | π/6 | √3/2 | 1/2 | √3/3 |
| C | 45° | π/4 | √2/2 | √2/2 | 1 |
| D | 60° | π/3 | 1/2 | √3/2 | √3 |
| E | 90° | π/2 | 0 | 1 | undefined |
| F | 120° | 2π/3 | −1/2 | √3/2 | −√3 |
| G | 135° | 3π/4 | −√2/2 | √2/2 | −1 |
| H | 150° | 5π/6 | −√3/2 | 1/2 | −√3/3 |
| I | 180° | π | −1 | 0 | 0 |
| J | 210° | 7π/6 | −√3/2 | −1/2 | √3/3 |
| K | 225° | 5π/4 | −√2/2 | −√2/2 | 1 |
| L | 240° | 4π/3 | −1/2 | −√3/2 | √3 |
| M | 270° | 3π/2 | 0 | −1 | undefined |
| N | 300° | 5π/3 | 1/2 | −√3/2 | −√3 |
| O | 315° | 7π/4 | √2/2 | −√2/2 | −1 |
| P | 330° | 11π/6 | √3/2 | −1/2 | −√3/3 |
Start with 30°, 45°, and 60°. Their sine values are 1/2, √2/2, and √3/2. Cosine uses the same three values in reverse. Reflect those points into the other quadrants and change the signs. A reference angle gives you the size; the quadrant gives you the signs.
FROM SCREEN TO STUDY SHEET
Take your practice to paper.
Print a blank unit circle with a place for degrees, radians, and coordinates. Use all 16 points or the quadrant selected in Customize. Add a separate answer key to check your work.
Choose “Save as PDF” in your print dialog to save a copy.
A FEW GOOD QUESTIONS
Unit Circle Quiz FAQ
What does this unit circle quiz cover?
Practice all core unit circle question types across five levels: positions, degree-radian conversions, coordinates in both directions, sine, cosine, tangent, reference angles, quadrant signs, and reverse problems with every solution in the interval. Final Challenge mixes all core types, while Advanced adds coterminal angles, secant, cosecant, and cotangent.
How does Fill the Circle work?
Select a lettered point and enter its degrees, radians, and coordinates. Save each point, then check the circle when you are ready. Each point has three items, so a full circle has 48 items. Unanswered items remain blank. You can correct your work, check again, or print a blank worksheet with an optional answer key.
Can I type answers instead of choosing them?
Yes. Select Type Answer above the choices. You can enter pi/6 or π/6, use sqrt(2) or √2, and write coordinates as (x, y). Equivalent forms such as 1/√2 and √2/2 are accepted. For reverse problems, separate every angle with commas; answer order does not matter. For tangent at 90° or 270°, enter undefined.
How does mistake review help?
Incorrect or skipped questions are saved in this browser and become due for review. Each review mixes the original question with related transfer practice, then checks the original again. Two correct answers without a hint schedule that item for a longer interval: 1, 3, 7, 14, then 30 days. These records are practice feedback, not a measure of ability.
Is this free, and do I need an account?
The quiz, fill-in circle, mistake review, and printable worksheets are free and require no account. Mistakes stay in this browser when storage is available. Clearing browser storage removes them; private browsing may not keep them. A shared link contains practice settings, not answers or personal results.