tanangle

Tanangle is a term used in geometry and computer science to denote the orientation angle of a two-dimensional vector or line, derived from the relationship between the coordinate components and the tangent function. In many contexts, tanangle is defined as the angle theta for which tan(theta) equals the ratio y/x, or equivalently theta = arctan2(y, x).

This construction ties directly to polar coordinates, where a point (x, y) is represented by its distance r and its angle theta. The function arctan2(y, x) returns theta in a standard range, such as (-pi, pi] or [0, 2pi), and handles the correct quadrant. For x ≠ 0, tan(theta) = y/x; for x = 0 the angle is pi/2 or -pi/2 depending on the sign of y.

Applications of tanangle appear in computer graphics, robotics, and geographic information systems, where it is useful for expressing direction, rotating objects, or converting Cartesian coordinates to polar form. It also provides a stable basis for angle normalization and directional planning.

Variants and considerations: tanangle depends on the chosen reference axis, and whether the angle is measured clockwise or counterclockwise. Implementations typically rely on the arctangent with two arguments to determine the correct quadrant. When converting to degrees, users must apply a consistent unit and handle wraparound at 360 degrees.

Etymology and usage: 'tanangle' is a portmanteau of tangent and angle and is not a universally standard term; it is largely descriptive and may be encountered as informal notation or in specific software libraries. Related concepts include the polar angle and the argument of a complex number.