Drag the point around the circle, type an angle in degrees or radians, or tap a special angle. You see the radian measure, coordinates (cos θ, sin θ) and the exact values of all six trig functions, and you can print a fully labeled unit circle chart.
Last updated:
Degrees
Radians
Point (cos θ, sin θ)
Quadrant
Reference angle
Coterminal angle
Function
Exact
Decimal
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How to use the Interactive Unit Circle
Move the angle: drag the point on the circle, use the arrow keys after focusing it, or tap one of the special-angle buttons.
Or type an angle such as 210, -45, 3pi/4 or 2.5 and choose degrees or radians.
Read the values: radians, coordinates, quadrant, reference angle and the exact and decimal values of sin, cos, tan, csc, sec and cot.
Change the labels on the circle to degrees, radians or coordinates and turn the triangle or tangent overlay on or off.
Print the chart for a complete labeled unit circle and value table, or download it as SVG.
Unit circle values for the special angles
Degrees
Radians
(cos θ, sin θ)
tan θ
0°
0
(1, 0)
0
30°
π/6
(√3/2, 1/2)
√3/3
45°
π/4
(√2/2, √2/2)
1
60°
π/3
(1/2, √3/2)
√3
90°
π/2
(0, 1)
undefined
120°
2π/3
(−1/2, √3/2)
−√3
135°
3π/4
(−√2/2, √2/2)
−1
150°
5π/6
(−√3/2, 1/2)
−√3/3
180°
π
(−1, 0)
0
210°
7π/6
(−√3/2, −1/2)
√3/3
225°
5π/4
(−√2/2, −√2/2)
1
240°
4π/3
(−1/2, −√3/2)
√3
270°
3π/2
(0, −1)
undefined
300°
5π/3
(1/2, −√3/2)
−√3
315°
7π/4
(√2/2, −√2/2)
−1
330°
11π/6
(√3/2, −1/2)
−√3/3
Key unit circle formulas
Point on the circle: (x, y) = (cos θ, sin θ), and x² + y² = 1, so sin²θ + cos²θ = 1.
Coterminal angles: θ + 360°·k (or θ + 2πk) end at the same point, so −30°, 330° and 690° share all trig values.
Arc length: on the unit circle the arc length equals the angle in radians, which is why radians are the natural unit.
A quick way to remember the circle
Learn the first quadrant only. The three special points are (√3/2, 1/2) at 30°, (√2/2, √2/2) at 45° and (1/2, √3/2) at 60°. Every other special point is a mirror image: in Quadrant II flip the sign of x, in Quadrant III flip both, in Quadrant IV flip y. The radian denominators follow the family: angles based on 30° use sixths (π/6, 5π/6, 7π/6, 11π/6), 45° uses quarters, and 60° uses thirds. Use the Degrees to Radians converter for any other angle and the Trigonometry Calculator to solve triangles.
Frequently asked questions
What is the unit circle?
The unit circle is a circle with radius 1 centered at the origin. For an angle θ measured counterclockwise from the positive x-axis, the point where the terminal side meets the circle has coordinates (cos θ, sin θ). This makes it a simple way to define and remember the trigonometric functions for any angle.
How do I convert degrees to radians?
Multiply by π/180. For example 150° × π/180 = 5π/6 ≈ 2.618 rad. To go back, multiply radians by 180/π. A full circle is 360° = 2π radians.
How do I find tan on the unit circle?
tan θ = sin θ / cos θ = y / x. Geometrically it is the length of the segment on the tangent line x = 1, from (1, 0) up to where the extended radius crosses it. It is undefined at 90° and 270°, where cos θ = 0.
What does ASTC (All Students Take Calculus) mean?
It tells you which functions are positive in each quadrant: in Quadrant I All are positive, in Quadrant II only Sine (and csc), in Quadrant III only Tangent (and cot), and in Quadrant IV only Cosine (and sec).
What is a reference angle?
The reference angle is the acute angle between the terminal side and the x-axis. It is θ in Quadrant I, 180° − θ in Quadrant II, θ − 180° in Quadrant III and 360° − θ in Quadrant IV. The trig values of θ equal those of its reference angle, with the sign set by the quadrant.
How do I memorize the special angle values?
For 0°, 30°, 45°, 60° and 90° the sines are √0/2, √1/2, √2/2, √3/2 and √4/2, that is 0, 1/2, √2/2, √3/2 and 1. The cosines are the same list in reverse order. Every other special angle uses these values with the sign of its quadrant.
Which angles have exact values here?
Every multiple of 15° (π/12) shows exact values, including 15° and 75°, for example sin 15° = (√6 − √2)/4 and tan 15° = 2 − √3. Other angles show decimal values rounded to 6 places.
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