Unit Circle Calculator
Unit Circle Calculator
Enter an angle in degrees or radians, and this calculator shows the (x, y) coordinates of that angle on the unit circle, along with its quadrant and reference angle, illustrated with a diagram.
On the unit circle — a circle of radius exactly 1 centered at the origin — the x-coordinate of any angle's position equals its cosine and the y-coordinate equals its sine, which is precisely why the unit circle is the standard visual tool for building intuition about how sine and cosine behave across all four quadrants, not just the acute angles covered by basic right-triangle trigonometry. Knowing which quadrant an angle falls into immediately tells you the sign of its sine and cosine — both positive in the first quadrant, only sine positive in the second, and so on — a pattern that becomes second nature once visualized on the circle rather than memorized as an abstract rule.
- On the unit circle (radius 1, centered at the origin), the x-coordinate of any angle equals its cosine, and the y-coordinate equals its sine, giving the point (cos θ, sin θ).
- The circle is divided into four quadrants, and knowing which quadrant an angle falls in tells you the sign of its sine and cosine — both positive in quadrant I, only sine positive in quadrant II, and so on.
- The reference angle is the acute angle (between 0° and 90°) formed with the x-axis, useful for relating any angle back to values you may already know for angles under 90°.
How do I find the coordinates of an angle on the unit circle?
Take the cosine of the angle for the x-coordinate and the sine for the y-coordinate — the point (cos θ, sin θ) always lies exactly on the unit circle.
What quadrant is 150° in, and what is its reference angle?
Quadrant II, with a reference angle of 30° (since 180° − 150° = 30°).
Unit Circle Calculator
Enter an angle in degrees or radians, and this calculator shows the (x, y) coordinates of that angle on the unit circle, along with its quadrant and reference angle, illustrated with a diagram.
On the unit circle — a circle of radius exactly 1 centered at the origin — the x-coordinate of any angle's position equals its cosine and the y-coordinate equals its sine, which is precisely why the unit circle is the standard visual tool for building intuition about how sine and cosine behave across all four quadrants, not just the acute angles covered by basic right-triangle trigonometry. Knowing which quadrant an angle falls into immediately tells you the sign of its sine and cosine — both positive in the first quadrant, only sine positive in the second, and so on — a pattern that becomes second nature once visualized on the circle rather than memorized as an abstract rule.
- On the unit circle (radius 1, centered at the origin), the x-coordinate of any angle equals its cosine, and the y-coordinate equals its sine, giving the point (cos θ, sin θ).
- The circle is divided into four quadrants, and knowing which quadrant an angle falls in tells you the sign of its sine and cosine — both positive in quadrant I, only sine positive in quadrant II, and so on.
- The reference angle is the acute angle (between 0° and 90°) formed with the x-axis, useful for relating any angle back to values you may already know for angles under 90°.
How do I find the coordinates of an angle on the unit circle?
Take the cosine of the angle for the x-coordinate and the sine for the y-coordinate — the point (cos θ, sin θ) always lies exactly on the unit circle.
What quadrant is 150° in, and what is its reference angle?
Quadrant II, with a reference angle of 30° (since 180° − 150° = 30°).