Unit Circle Calculator

sin(θ)
cos(θ)
tan(θ)
Quadrant
Point on Unit Circle

How It Works

This unit circle calculator uses established formulas to provide accurate results.

The basic rule:

  • Point on unit circle: (cos θ, sin θ)
  • tan θ = sin θ / cos θ
  • sin²θ + cos²θ = 1
  • Reference angle: acute angle to x-axis

Results are estimates. Consult a professional for critical decisions.

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Frequently Asked Questions

What is the unit circle?

The unit circle is a circle with radius 1 centered at the origin (0,0). Any angle θ corresponds to a point (cos θ, sin θ) on the circle. It is the foundation for understanding trigonometric functions.

How do I determine the quadrant of an angle?

Quadrant I: 0° to 90° (sin+, cos+). Quadrant II: 90° to 180° (sin+, cos-). Quadrant III: 180° to 270° (sin-, cos-). Quadrant IV: 270° to 360° (sin-, cos+). Remember: All Students Take Calculus.

What are the key angles to memorize on the unit circle?

The most important angles are 0°, 30°, 45°, 60°, 90°, and their counterparts in each quadrant (120°, 135°, 150°, 180°, 210°, 225°, 240°, 270°, 300°, 315°, 330°, 360°).

What is a reference angle?

A reference angle is the acute angle formed between the terminal side of your angle and the x-axis. It helps find trig values for angles in any quadrant using known values from Quadrant I.