Introduction to the Unit Circle in Trigonometry
The unit circle is one of the most important conceptual structures in geometry and trigonometry. It is defined as a circle with a radius of exactly one ($r = 1$), centered at the origin $(0, 0)$ in the Cartesian coordinate plane. While basic trigonometry defines sine, cosine, and tangent using right triangles (restricted to angles between 0° and 90°), the unit circle extends these definitions to any real angle—positive or negative—expressed in degrees or radians.
On the unit circle, any angle $\theta$ corresponds to a coordinate point $(x, y)$ where the terminal ray intersects the circle. By definition, the coordinates represent the cosine and sine of the angle: $x = \cos(\theta)$ and $y = \sin(\theta)$. The tangent is defined as the ratio of these coordinates: $\tan(\theta) = y/x$. This circle forms the foundation for graphing trigonometric functions, solving trigonometric equations, and analyzing wave harmonics in physics and engineering.
This calculator evaluates trigonometric values for any target angle. By inputting the angle in degrees or radians, the solver computes the coordinate values, reference angle, quadrant, and the reciprocal trig functions (cosecant, secant, cotangent).