Unit Circle Calculator
Find a point on the unit circle from an angle in degrees or radians.
Formula
x = cos θ; y = sin θ; θ is reduced to [0, 2π).; complementary angle = 90° − θ (before reduction).
Reduced angle ≈ ((30)-360×floor((30)÷360))×pi÷180 · x = cos θ ≈ cos((0.5235987756)) · y = sin θ ≈ sin((0.5235987756)) · Complementary angle (degrees) ≈ 90-(30)
How to use
- Enter the angle and unit.
- Use a negative angle for clockwise rotation.
- Read x, y and the reduced angle in radians.
Examples
- 90° gives (x,y) = (0,1) and a reduced angle of π/2.
Frequently asked questions
What is the radius?
The circle has radius 1 and center (0,0).
Which coordinate is sine?
The y-coordinate is sine; x is cosine.
Do whole turns change the point?
No. Adding 360° or 2π radians returns to the same point.
What are the cofunction identities?
At complementary angles θ and 90°−θ: sinθ=cos(90°−θ), cosθ=sin(90°−θ), tanθ=cot(90°−θ), secθ=csc(90°−θ), wherever defined.
Sources
Updated: