Unit Circle Calculator

The unit circle is a circle with radius one centered at the origin of a coordinate plane. Every angle determines a point on its circumference. The horizontal coordinate of that point is cosine, and the vertical coordinate is sine. Tangent is the ratio of sine to cosine whenever cosine is not zero. This geometric model connects angles, coordinates, periodic motion, and trigonometric functions in one picture. This calculator accepts angles in degrees or radians. Degrees divide a complete rotation into 360 parts, while radians measure arc length relative to radius and divide a complete rotation into two pi radians. When degrees are selected, the calculator converts the entered value to radians before applying the standard sine and cosine functions. It then reports the point as an ordered pair, followed by sine, cosine, and tangent rounded to six decimal places. Angles can be positive, negative, or larger than one full revolution. Trigonometric functions are periodic, so coterminal angles produce the same coordinates. For example, 30 degrees, 390 degrees, and negative 330 degrees end at the same point. At 90 and 270 degrees, cosine is zero, so tangent involves division by zero and is shown as undefined. Very small floating-point artifacts near exact zeros are cleaned up for a more useful display. The unit circle is fundamental in geometry, calculus, physics, engineering, and signal analysis. It helps explain signs in each quadrant, reciprocal functions, identities, waves, rotations, and complex numbers. Students can use this tool to check special-angle work or explore unfamiliar angles. Professionals can quickly convert an angular input into normalized Cartesian components. Although decimal values are convenient, exact forms such as one half or square root expressions remain valuable when doing symbolic mathematics. Use the calculator as a numerical companion to the geometric definitions, and always confirm whether a problem expects degrees or radians before interpreting the result.