Unit Circle Calculator

Drag the angle, see exact trig values — AI explains everything

This interactive unit circle calculator lets you explore every angle from 0° to 360°. Drag the θ slider and watch the blue point trace the unit circle x^2 + y^2 = 1 on a polar grid.

The trig readout panel (top-left) shows exact values: sin θ, cos θ, tan θ, the quadrant, and the radian equivalent. At key angles (30°, 45°, 60°, 90°, ...) you'll see the famous exact fractions like √2/2 and √3/2.

The muted dots mark the key angles for reference. Ask the AI assistant anything: "What's sin(150°)?", "Why is tan(90°) undefined?", "Show me the reference triangle at 225°." The AI draws directly on the graph to explain.

Related Topics

Unit Circle LessonSine & CosinePythagorean Theorem

Suggested Lessons

Slope Quadratic Equations Unit Circle Word Problems
What is the unit circle?
The unit circle is a circle centered at the origin (0, 0) with a radius of exactly 1. Its equation is x^2 + y^2 = 1. Every point on it can be written as (cos θ, sin θ).
What are the exact values at key angles?
At 30°: (√3/2, 1/2). At 45°: (√2/2, √2/2). At 60°: (1/2, √3/2). At 90°: (0, 1). These values repeat with sign changes in other quadrants. Memorize the first quadrant and you know them all.
Why is tangent undefined at 90° and 270°?
Tangent = sin θ / cos θ. At 90° and 270°, cos θ = 0, so you're dividing by zero. Geometrically, the tangent line at the top and bottom of the circle is vertical — it has no finite slope.
What is a reference angle?
The reference angle is the acute angle (0°–90°) between the terminal side of your angle and the x-axis. For example, 150° has reference angle 30°, and 225° has reference angle 45°. Trig values of the original angle equal those of the reference angle, with signs determined by the quadrant.
How do I convert between degrees and radians?
Multiply degrees by \pi/180 to get radians. So 90° = π/2, 60° = π/3, 45° = π/4, 30° = π/6. A full circle is 360° = 2π radians.
What can it graph?
It can plot explicit, implicit, and parametric functions, add points and geometry, and animate sliders on the same graph.
Can I use voice or a photo?
Yes. You can talk to the tutor, upload a worksheet or handwritten problem, and let the graph update from that input.
Will it explain the steps?
Yes. The AI explains what it is drawing and why, so you see the answer on the graph instead of getting only a final number.