The ATAN() function in SQLite calculates the arc tangent (inverse tangent) of a given numeric value. The result is the angle in radians whose tangent is the specified number.

Syntax

ATAN(X)

Where X is the numeric value for which you want to calculate the arc tangent. This value can be any real number (positive, negative, or zero).

The result will be an angle in radians between -π/2 and π/2 (approximately -1.5708 and 1.5708).

Example 1

Here’s a quick example to demonstrate how it works:

SELECT ATAN(5);

Output:

1.37340076694502

Example 2

Suppose we have a table angles with a column tan_value that contains tangent values, and we want to find the corresponding angle in radians for these values.

CREATE TABLE angles (tan_value REAL);

INSERT INTO angles (tan_value) VALUES (1), (0.5), (0), (-0.5), (-1);

Now, we can use ATAN() to calculate the angle in radians for each tangent value:

SELECT tan_value, ATAN(tan_value) AS angle_in_radians
FROM angles;

Output:

tan_value  angle_in_radians  
---------  ------------------
1.0        0.785398163397448 
0.5        0.463647609000806 
0.0        0.0               
-0.5       -0.463647609000806
-1.0       -0.785398163397448

In this example:

• When tan_value is 1, the result is approximately 0.785398163397448 radians (π/4), since the tangent of π/4 is 1.
• When tan_value is 0.5, the angle is approximately 0.463647609000806 radians.
• When tan_value is 0, the angle is 0 radians because the tangent of 0 radians is 0.
• When tan_value is -0.5, the angle is approximately -0.463647609000806 radians.
• Similarly, -1 corresponds to approximately -0.785398163397448 radians.

The ATAN() function is commonly used in trigonometry and geometry, especially when converting a tangent value back to an angle, such as in navigation, physics, and engineering calculations.