Trigonometry Unit Circle

Unit Circle — Exact Trig Values

Enter any angle in degrees or radians to find all six trig functions. For standard angles (multiples of 30° and 45°), exact fraction forms like √2/2 and √3/2 are shown.

Exact values for standard angles
All 6 trig functions
Interactive unit circle
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Angle Input
Angle value
Preset angles
Results
Enter an angle above to see all six trig values.
Unit Circle Point (cos θ, sin θ)
sin θ
cos θ
tan θ
csc θ
sec θ
cot θ
Step-by-Step Solution
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Unit Circle Diagram
The Unit Circle
For angle θ: point on unit circle = (cos θ, sin θ) sin²θ + cos²θ = 1  (Pythagorean identity)

The unit circle has radius 1 centered at the origin. Every angle θ corresponds to a point (x, y) = (cos θ, sin θ) on the circle. The x-coordinate is always cos θ and the y-coordinate is always sin θ.

For standard angles (multiples of 30° = π/6 and 45° = π/4), exact values are expressible using simple fractions and square roots: 1/2, √2/2, and √3/2.

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