Unit Circle Calculator

Find exact trigonometric values and coordinates for any angle on the unit circle. Essential for students and professionals in mathematics, physics, and engineering.

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Understanding the Unit Circle

The unit circle is a fundamental concept in trigonometry where a circle with radius 1 is centered at the origin (0,0). Any point on the circle corresponds to (cos θ, sin θ) where θ is the angle from the positive x-axis.

Common Reference Angles

Degrees	Radians	Coordinates	sin θ	cos θ	tan θ
0°	0	(1, 0)	0	1	0
30°	π/6	(√3/2, 1/2)	1/2	√3/2	√3/3
45°	π/4	(√2/2, √2/2)	√2/2	√2/2	1
60°	π/3	(1/2, √3/2)	√3/2	1/2	√3
90°	π/2	(0, 1)	1	0	undefined

Interactive Quadrant Explorer

Frequently Asked Questions

How are negative angles handled?

Negative angles are measured clockwise from the positive x-axis. We convert them to their positive equivalent by adding 360° (or 2π radians).

What about angles greater than 360°?

Angles are normalized to their equivalent between 0° and 360° using modulo arithmetic to find the corresponding position on the unit circle.

How precise are the calculations?

Exact values are shown for common angles (30°, 45°, 60°, etc.). For other angles, we show decimal approximations with configurable precision.

For informational and educational purposes only. Not professional advice. Results may vary based on input precision and calculation methods.

References: Trigonometric Functions (Standard Mathematical Tables), Unit Circle Geometry (Euclidean Mathematics), Polar Coordinate System (Analytic Geometry)

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Unit Circle Calculator - Exact Values and Coordinates

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