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Unit Circle Calculator — How It Works

Unit Circle Calculator math calculator geometry

Unit Circle Calculator — How It Works

The unit circle is a circle of radius 1 centered at the origin. Every angle θ corresponds to a point (cos θ, sin θ) on that circle.

How it works

Enter an angle in degrees. The tool computes:

  • Coordinates: (cos θ, sin θ)
  • tan θ = sin θ / cos θ (undefined when cos θ = 0)
  • Quadrant: which of the four quadrants (I-IV) the point falls in, or “on axis” for multiples of 90°

Example

θ = 45°  →  (cos 45°, sin 45°) ≈ (0.7071, 0.7071)  →  Quadrant I
θ = 135° →  (cos 135°, sin 135°) ≈ (-0.7071, 0.7071) → Quadrant II

Why it matters

The unit circle is the foundation of trigonometry — it extends sine and cosine to angles beyond 0°-90° and shows how they relate to circular motion.

Try the Unit Circle Calculator — instant results, no sign-up.

FAQ

Is this free?

Yes — the Unit Circle Calculator runs entirely in your browser, no sign-up required.