MySQL ATAN() Function

The ATAN() function calculates the arc tangent (inverse tangent) of one or two numeric values.

Syntax

ATAN(number)

or

ATAN(a, b)

Definition and Usage

• The ATAN() function returns the arc tangent (inverse tangent) of a number or the result of dividing two numbers (a / b).
• If one parameter (number) is provided, it returns the arc tangent of that value.
• If two parameters (a, b) are provided, it calculates the arc tangent of the quotient a / b.

Parameter Values

Technical Details

• Works in: From MySQL 4.0
• Result:
  • If number is used, the result is in radians within the range [−π2,π2][- \frac{\pi}{2}, \frac{\pi}{2}].
  • If a, b are used, the result is in radians within the range [−π,π][- \pi, \pi].

Examples

Example 1: Arc tangent of a single value

SELECT ATAN(2.5);

Result:

1.1902899496825317

Example 2: Arc tangent of a negative value

SELECT ATAN(-0.8);

Result:

-0.6747409422235527

Example 3: Arc tangent of two values

SELECT ATAN(-0.8, 2);

Result:

-0.3805063771123649

Example 4: Arc tangent of 0

SELECT ATAN(0);

Result:

0

Usage Notes

1. Radians to Degrees Conversion: Multiply the result by 180π\frac{180}{\pi} to convert to degrees:

   SELECT ATAN(2.5) * (180 / PI());
   

   Result in degrees:

   68.19859051364818
   

2. Trigonometric Applications:

   • Use ATAN() for geometric calculations, such as finding angles in triangles.
   • The two-parameter version (ATAN(a, b)) is useful for determining the direction of a vector.

3. Null Handling:

   • If the parameter(s) are NULL, the function returns NULL.

Example Query with Conversion

To get the arc tangent of several values in both radians and degrees:

SELECT 
    ATAN(2.5) AS Radians,
    ATAN(2.5) * (180 / PI()) AS Degrees;

Result:

Radians: 1.1902899496825317
Degrees: 68.19859051364818