atan2yy

atan2yy is a mathematical function that calculates the arctangent of the ratio y/x, but also takes into account the signs of both y and x to determine the correct quadrant of the resulting angle. This distinguishes it from the standard atan(y/x) function, which can only return values in the range of -pi/2 to pi/2 radians (or -90 to 90 degrees).

The atan2yy function typically returns an angle in the range of -pi to pi radians (or -180 to 180 degrees). This broader range is crucial for accurately representing angles in all four quadrants of a Cartesian coordinate system. For example, if x is positive and y is positive, the angle will be in the first quadrant (0 to pi/2). If x is negative and y is positive, the angle will be in the second quadrant (pi/2 to pi). If both x and y are negative, the angle will be in the third quadrant (-pi to -pi/2), and if x is positive and y is negative, the angle will be in the fourth quadrant (-pi/2 to 0).

The primary use of atan2yy is in trigonometry, physics, and computer graphics, particularly when dealing with vectors, rotations, and coordinate transformations. It is commonly found in programming languages and mathematical libraries. When implementing atan2yy, special care is usually taken for the case where x is zero to avoid division by zero errors. If x is zero, the angle is typically pi/2 if y is positive, -pi/2 if y is negative, and undefined or zero if both x and y are zero.