Unit Circle Calculator
Find the unit circle point from an angle
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Unit Circle Formula
(x, y) = (cos θ, sin θ)
The unit circle has radius one and is centered at the origin. For any angle θ, cosine gives the x-coordinate and sine gives the y-coordinate.
⚠ Enter the angle in degrees. The calculator converts it to radians internally before evaluating sine and cosine.
How the Unit Circle Works
An angle rotates from the positive x-axis to a point on the circle. The coordinates of that point define cosine and sine for the angle.
Radius One
Every point is one unit from the origin.
Cosine
The x-coordinate is cos θ.
Sine
The y-coordinate is sin θ.
Radians
Angles can be converted to radian measure.
💡 Example: For 60°, the unit circle point is approximately (0.5, 0.866025).
Applications of Unit Circle
Trig Values Rotations Graphing Calculus
Frequently Asked Questions
What is a unit circle calculator?▼
It finds the point (cos θ, sin θ) on the unit circle for a given angle.
What is the unit circle formula?▼
The coordinate formula is (x, y) = (cos θ, sin θ).
How do I use this calculator?▼
Enter an angle in degrees and click Calculate.
Why is the radius one?▼
The unit circle has radius 1, which makes sine and cosine equal to the y and x coordinates.
Where is the unit circle used?▼
It is used in trigonometry, graphing, radians, waves, rotations, and calculus.
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