Unit Circle Calculator
Find the point (cos θ, sin θ) on the unit circle for any angle, with exact coordinates, quadrant, reference angle and all six functions.
Change the values and press Calculate to work out your own figures.
Enter an angle and choose degrees or radians.
| Function | Value | Exact |
|---|---|---|
| sin(θ) | -0.7071067812 | −√2/2 |
| cos(θ) | -0.7071067812 | −√2/2 |
| tan(θ) | 1 | 1 |
| csc(θ) | -1.414213562 | −√2 |
| sec(θ) | -1.414213562 | −√2 |
| cot(θ) | 1 | 1 |
Show the working
- x = cos θ, y = sin θ
- θ = 225° = 3.926990817 rad = 5π/4
How to use it
Enter an angle and choose degrees or radians.
Enter the values you know (decimals, fractions, surds such as 2√5, or angles such as π/3 in radians). Show the working gives the rule used at each step.
Key facts
(x, y) = (cos θ, sin θ); x² + y² = 1
Reading the circle
The point at angle θ from the positive x-axis has coordinates (cos θ, sin θ); its signs give the quadrant.
Questions
What is the point at 225°?
(−√2/2, −√2/2).
And at 5π/6?
(−√3/2, 1/2).
Formulas
(x, y) = (cos θ, sin θ); x² + y² = 1
Sources
Limitations
- Angles can be typed in degrees or radians; radians may be written with π (π/3, 2pi/3).