Why is the unit circle important?

The unit circle extends trigonometry beyond triangles. Every angle and its trig values map directly to circle coordinates.

What does the Pythagorean identity sin²θ + cos²θ = 1 represent on the unit circle?

It states that any point (cos θ, sin θ) on the unit circle satisfies the circle equation x² + y² = 1.

How many degrees are in one full rotation on the unit circle?

360° or 2π radians. After that, angles repeat with the same sine and cosine values.

Mathematics

Unit Circle Calculator

Angle

Common Angles Reference

Angle

sin

cos

tan

0°

30°

0.5

0.866

0.577

45°

0.707

60°

0.866

0.5

1.732

90°

Undef

180°

-1

270°

-1

Undef

The unit circle is a circle with radius 1 centred at the origin. It provides the foundation for trigonometry — the sine and cosine of any angle equal the y and x coordinates of the corresponding point on the circle.

Symbol	Name	Unit	Description
θ	angle from positive x-axis	radians or degrees	—
x	x-coordinate (cosine value)	dimensionless	—
y	y-coordinate (sine value)	dimensionless	—

Angle (°)	sin	cos	tan
0	0	1	0
30	0.5	0.866	0.577
45	0.707	0.707	1
60	0.866	0.5	1.732
90	1	0	undef
180	0	−1	0

References

›Unit circle — Khan Academy

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