Unit Circle Calculator
Look up exact sin, cos, tan values and coordinates for standard unit-circle angles.
Inputs
sin θ
0.7071067812
cos θ
0.7071067812
tan θ
1
Quadrant
I
Reference angle
45.0000°
Radians
0.78539816
Step by step
Normalised angle
= 45° = 0.785398 rad
Quadrant
= I
Reference angle
= 45°
Coordinates (cos θ, sin θ)
= (0.7071067812, 0.7071067812)
How it works
The unit circle is a circle of radius 1 centred at the origin. Any angle θ maps to the point (cos θ, sin θ). The reference angle is the acute angle formed with the x-axis; the quadrant determines the sign of each function.
Formula
Unit circle coordinates
(x, y) = (cos θ, sin θ) on a circle of radius 1
- θ
- Angle from positive x-axis
- x
- cos θ
- y
- sin θ
Frequently Asked Questions
What are the standard unit circle angles?
0°, 30°, 45°, 60°, 90° and their counterparts in each quadrant: 120°, 135°, 150°, 180°, 210°, 225°, 240°, 270°, 300°, 315°, 330°, 360°.
How do I find the reference angle?
In Q1: ref = θ; in Q2: ref = 180° − θ; in Q3: ref = θ − 180°; in Q4: ref = 360° − θ.