Finance Health Math Other Blog
Login

Unit Circle Calculator

Explore the unit circle with special angles

Enter an angle or select a special angle to see unit circle values.

Unit Circle Reference

What is the Unit Circle?

The **unit circle** is a circle with radius 1 centered at the origin (0,0) of a coordinate plane. It's fundamental in trigonometry because any point on the circle can be described using an angle and provides the values of sine and cosine for that angle.

Key Properties:

  • Radius = 1
  • Center at (0, 0)
  • Equation: x² + y² = 1
  • For any angle θ: (cos θ, sin θ) is on the circle

Special Angles

Angle Radians sin θ cos θ tan θ
0° 0 0 1 0
30° π/6 1/2 √3/2 √3/3
45° π/4 √2/2 √2/2 1
60° π/3 √3/2 1/2 √3
90° π/2 1 0 undefined

Quadrants

  • Quadrant I (0° to 90°): Both sin and cos are positive
  • Quadrant II (90° to 180°): sin positive, cos negative
  • Quadrant III (180° to 270°): Both sin and cos are negative
  • Quadrant IV (270° to 360°): sin negative, cos positive
Quick Tips
  • Coordinates
    Any point on the unit circle is (cos θ, sin θ).
  • Reference Angle
    The acute angle to the x-axis, always between 0° and 90°.
  • ASTC Rule
    All Students Take Calculus: which trig functions are positive in each quadrant.
Memory Aid

30-60-90 Triangle:

Sides are in ratio 1 : √3 : 2

45-45-90 Triangle:

Sides are in ratio 1 : 1 : √2

The Unit Circle

The unit circle is one of the most important tools in trigonometry. It connects angles, coordinates, and trig functions in a beautiful geometric way.

Sign Rules
Quadrant I All positive (sin+, cos+, tan+)
Quadrant II Sin positive (sin+, cos-, tan-)
Quadrant III Tan positive (sin-, cos-, tan+)
Quadrant IV Cos positive (sin-, cos+, tan-)
Related Tools
Trigonometry Calculator Pythagorean Theorem Scientific Calculator
Learn More

Unit Circle Resources:

Did You Know?

The unit circle makes it easy to find trig values for any angle, not just acute angles. It extends trigonometry beyond right triangles!