SQL Server ATN2() Function

 The ATN2() function in SQL Server calculates the angle (in radians) whose tangent is the ratio of two specified numbers, y and x. This is known as the two-argument arctangent function.

Syntax

ATN2 ( float_expression_y, float_expression_x )

• float_expression_y: The y-coordinate of the point.
• float_expression_x: The x-coordinate of the point.

Functionality

The ATN2(y, x) function calculates the arctangent of the angle between the positive x-axis and the ray from the origin to the point (x, y) in a Cartesian plane. The function:

• Returns values in the range -π to π radians.
• Takes into account the signs of x and y to determine the correct quadrant of the angle.

Example

Here are some usage examples of the ATN2() function:

Basic Example

SELECT ATN2(1.0, 1.0) AS Result;

Output: Approximately 0.785398 (which is π/4 radians).

When x and y are in different quadrants

SELECT ATN2(-1.0, 1.0) AS Result;

Output: Approximately -0.785398 (negative π/4 radians).

Using zero values

SELECT ATN2(0.0, 1.0) AS Result;

Output: 0.0 (angle is zero when y is 0).

SELECT ATN2(1.0, 0.0) AS Result;

Output: 1.570796 (which is π/2 radians, representing a vertical angle).

Practical Applications

1. Geographic Calculations: Compute bearings or angles based on coordinates.
2. Vector Calculations: Determine the direction of a vector in 2D space.
3. Graphics: Calculate angles for rotations or projections.

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