Unit Circle Calculator
Find sin, cos and tan for any angle on the unit circle, with exact values for special angles.
About the Unit Circle Calculator
On a circle of radius 1 centred at the origin, the point at angle θ (measured anticlockwise from the positive x-axis) is (cos θ, sin θ), and tan θ = sin θ ÷ cos θ. Exact values exist for multiples of 15°; the signs depend on the quadrant (“All Students Take Calculus”: all positive in I, sin in II, tan in III, cos in IV).
The formula
(x, y) = (cos θ, sin θ); tan θ = y ÷ x; radians = degrees × π ÷ 180
Special angles
| Degrees | Radians | sin | cos | tan |
|---|---|---|---|---|
| 0 | 0 | 0 | 1 | 0 |
| 30 | π/6 | 1/2 | √3/2 | √3/3 |
| 45 | π/4 | √2/2 | √2/2 | 1 |
| 60 | π/3 | √3/2 | 1/2 | √3 |
| 90 | π/2 | 1 | 0 | undefined |
Worked example
Example: Point on the unit circle = (-0.984808, 0.173648)
- Inputs: Angle: 170; In: Degrees.
- Formula: (x, y) = (cos θ, sin θ); tan θ = y ÷ x; radians = degrees × π ÷ 180
- Result: Point on the unit circle = (-0.984808, 0.173648)
- sin: 0.1736481777
- cos: -0.984807753
- tan: -0.1763269807
Questions people ask
What is sin 150°?
1/2, since its reference angle is 30° and sine is positive in quadrant II.
How do I enter π/3 radians?
Choose radians and enter 1/3 as 0.333333, or use degrees (60).