In mathematics, the trigonometric functions (also called the circular functions) are functions of an angle.
The most familiar trigonometric functions are the sine, cosine, and tangent. In the context of the standard unit circle (a circle with radius 1 unit), where a triangle is formed by a ray originating at the origin and making some angle with the x-axis, the sine of the angle gives the length of the y-component (the opposite to the angle or the rise) of the triangle, the cosine gives the length of the x-component (the adjacent of the angle or the run), and the tangent function gives the slope (y-component divided by the x-component). More precise definitions are detailed below.

The values of sine represent the vertical coordinate of a point on the unit circle as it moves counterclockwise from the positive x-axis. They range from -1 to 1, indicating how far up or down the point is relative to the center of the circle.