ATAN2

Updated 2024-03-23 22:17:24.823000

Syntax

SELECT [wct].[ATAN2] (
   <@y, float,>
  ,<@x, float,>)

Description

Use the scalar function ATAN2 to calculate a numeric value between -π and π representing the angle θ of a (x, y) point and positive x-axis.

Arguments

@x

The x coordinate of a point

@y

The y coordinate of a point

Return Type

float

Remarks

If @y is 0 and @x is not negative, θ = 0.

If @y is 0 and @x is negative, θ = π.

If @y is positive and @x is 0, θ = π/2.

If @y is negative and @x is 0, θ = -π/2.

If @y is 0 and @x is 0, θ = 0.

If @y IS NULL or @x IS NULL, θ = NULL.

Note that this implementation is different than the Excel implementation which is ATAN2(x,y)

Examples

Example #1

SELECT wct.ATAN2(-0.9, -0.9) as theta1,
       wct.ATAN2(1.2, 1.5) as theta2,
       wct.ATAN2(1.2, -1.5) as theta3

This produces the following result.

                theta1                 theta2                 theta3
---------------------- ---------------------- ----------------------
     -2.35619449019234      0.674740942223553       2.46685171136624

Example #2

SELECT y,
       x,
       wct.ATAN2(y, x) as theta
FROM
(
    VALUES
        (1, 6),
        (2, 3),
        (3, 7),
        (4, 8)
) n (y, x)

This produces the following result.

          y           x                  theta
----------- ----------- ----------------------
          1           6      0.165148677414627
          2           3      0.588002603547568
          3           7      0.404891786285083
          4           8      0.463647609000806

See Also

ATANH - Calculate the inverse hyperbolic tangent of a number.