ATAN

Description

Return the arctangent value.

• When there is only one parameter: Return the arctangent of x, with the result range of [-π/2, π/2]

• When there are two parameters: Return the arctangent of y/x, with the same behavior as ATAN2(y, x), with the result range of [-π, π]

Syntax

ATAN([<y>, ]<x>)

Parameters

Parameter	Description
<x>	When there is only one parameter, it indicates the value that needs to be calculated as the arctangent; when there are two parameters, it indicates the horizontal coordinate (or x-value), the distance along the x-axis from the origin (0,0).
<y>	Optional, representing the vertical coordinate (or y-value), the distance along the y-axis from the origin (0,0)

Return Value

The atan value of parameter x.

Special Cases

Single-parameter version

• When x is NaN, returns NaN
• When x is positive infinity, returns π/2 (approximately 1.570796326794897)
• When x is negative infinity, returns -π/2 (approximately -1.570796326794897)
• When x is NULL, returns NULL

Two-parameter version

• If y or x is NaN, returns NaN
• If x > 0 and y = ±0.0, returns ±0 (sign follows y)
• If x = 0.0 (either +0.0 or -0.0) and y > 0, returns π/2 (about 1.570796326794897)
• If x = 0.0 (either +0.0 or -0.0) and y < 0, returns -π/2 (about -1.570796326794897)
• If x < 0 and y = +0.0, returns π (about 3.141592653589793); if x < 0 and y = -0.0, returns -π
• If y = +Infinity and x is finite, returns π/2; if y = -Infinity and x is finite, returns -π/2
• If y = +Infinity and x = +Infinity, returns π/4 (about 0.7853981633974483)
• If y = -Infinity and x = +Infinity, returns -π/4 (about -0.7853981633974483)
• If y = +Infinity and x = -Infinity, returns 3π/4 (about 2.356194490192345)
• If y = -Infinity and x = -Infinity, returns -3π/4 (about -2.356194490192345)
• If x = +Infinity and finite y > 0, returns 0; if finite y < 0, returns -0
• If x = -Infinity and finite y > 0, returns π; if finite y < 0, returns -π
• If y or x is NULL, returns NULL

Examples

select atan(0);

+-----------+
| atan(0.0) |
+-----------+
|         0 |
+-----------+

select atan(2);

+--------------------+
| atan(2.0)          |
+--------------------+
| 1.1071487177940904 |
+--------------------+

select atan(cast('nan' as double));

+-----------------------------+
| atan(cast('nan' AS DOUBLE)) |
+-----------------------------+
| NaN                         |
+-----------------------------+

select atan(cast('inf' as double));

+-----------------------------+
| atan(cast('inf' AS DOUBLE)) |
+-----------------------------+
| 1.570796326794897           |
+-----------------------------+

select atan(cast('-inf' as double));

+------------------------------+
| atan(cast('-inf' AS DOUBLE)) |
+------------------------------+
| -1.570796326794897           |
+------------------------------+