The ATANH() function in SQLite calculates the inverse hyperbolic tangent of a given numeric value. The result is the value whose hyperbolic tangent is the specified number.

Syntax

ATANH(X)

Where X is the numeric value for which you want to calculate the inverse hyperbolic tangent. This value must be between -1 and 1, exclusive, because the hyperbolic tangent is undefined outside this range.

The result will be a real number that represents the angle in hyperbolic space, in terms of radians.

Example 1

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

SELECT ATANH(0.35);

Output:

0.365443754271396

Example 2

Suppose we have a table hyperbolic_values with a column value containing values within the range (-1, 1). We want to calculate the inverse hyperbolic tangent for each of these values.

CREATE TABLE hyperbolic_values (value REAL);

INSERT INTO hyperbolic_values (value) VALUES (0.5), (-0.5), (0.9), (-0.9);

Now, we can use ATANH() to calculate the inverse hyperbolic tangent for each value:

SELECT value, ATANH(value) AS inverse_hyperbolic_tangent
FROM hyperbolic_values;

Output:

value  inverse_hyperbolic_tangent
-----  --------------------------
0.5    0.549306144334055         
-0.5   -0.549306144334055        
0.9    1.47221948958322          
-0.9   -1.47221948958322         

In this example:

• For a value of 0.5, ATANH(0.5) returns approximately 0.549306144334055 radians.
• For -0.5, the result is approximately -0.549306144334055 radians.
• A value of 0.9 returns approximately 1.47221948958322 radians.
• Similarly, -0.9 corresponds to approximately -1.47221948958322 radians.

The ATANH() function is useful in advanced mathematical and engineering fields, particularly in physics and complex analysis, where hyperbolic functions and their inverses play an important role.