Unit Circle Calculator

Formula

How this is calculated

The unit circle is the circle of radius 1 centred at the origin. Any angle θ, measured counter-clockwise from the positive x-axis, corresponds to a single point on this circle whose coordinates are exactly (cos θ, sin θ). The Angle input accepts the angle value and the unit selector chooses whether it is in degrees or radians; degrees are converted to radians internally with t = angle × π / 180 before evaluating the trigonometric functions.

The x-coordinate equals cos θ and the y-coordinate equals sin θ, both of which always lie between -1 and 1. The tangent is computed as sin θ / cos θ, which represents the slope of the radius line to the point. When cos θ = 0 (at 90° and 270°, or π/2 and 3π/2) the tangent is undefined because of division by zero, so the calculator reports it as undefined instead of a number.

The plot draws the full unit circle from sampled cosine and sine values, the radius line from the origin to the computed point, and marks the point itself. Values extremely close to zero are snapped to exactly 0 to avoid tiny floating-point artefacts such as 6.12e-17 appearing in place of 0.