The SINH() function in SQLite calculates the hyperbolic sine of a value. The hyperbolic sine is a mathematical function that can return any real number and grows exponentially as its input increases or decreases.

Syntax

SINH(x)

Where x is a numeric expression.

Example 1

Here’s a simple example to demonstrate:

SELECT SINH(3);

Output:

+------------------+
|     SINH(3)      |
+------------------+
| 10.0178749274099 |
+------------------+

Example 2

Here are a few calculations of interest:

SELECT 
       SINH(0),
       SINH(-2),
       -SINH(2),
       SINH(-2) = -SINH(2);

Output:

+---------+-------------------+-------------------+---------------------+
| SINH(0) |     SINH(-2)      |     -SINH(2)      | SINH(-2) = -SINH(2) |
+---------+-------------------+-------------------+---------------------+
| 0.0     | -3.62686040784702 | -3.62686040784702 | 1                   |
+---------+-------------------+-------------------+---------------------+

Example 3

Let’s explore how SINH() behaves with different input values:

-- Create a test table with various numbers
CREATE TABLE test_values (
    value_id INTEGER PRIMARY KEY,
    x FLOAT
);

-- Insert some test values
INSERT INTO test_values (x) VALUES 
    (-2),
    (-1),
    (-0.5),
    (0),
    (0.5),
    (1),
    (2);

-- Calculate hyperbolic sine values
SELECT 
    x,
    ROUND(SINH(x), 6) as sinh_value
FROM test_values;

Output:

+------+------------+
|  x   | sinh_value |
+------+------------+
| -2.0 | -3.62686   |
| -1.0 | -1.175201  |
| -0.5 | -0.521095  |
| 0.0  | 0.0        |
| 0.5  | 0.521095   |
| 1.0  | 1.175201   |
| 2.0  | 3.62686    |
+------+------------+

Output Grows Exponentially

The output of SINH() grows exponentially as the input increases:

SELECT 
       SINH(1),
       SINH(2),
       SINH(3),
       SINH(4),
       SINH(5);

Output:

+-----------------+------------------+------------------+------------------+------------------+
|     SINH(1)     |     SINH(2)      |     SINH(3)      |     SINH(4)      |     SINH(5)      |
+-----------------+------------------+------------------+------------------+------------------+
| 1.1752011936438 | 3.62686040784702 | 10.0178749274099 | 27.2899171971278 | 74.2032105777888 |
+-----------------+------------------+------------------+------------------+------------------+

Common Use Cases

SINH() is commonly used in:

• Scientific calculations
• Engineering applications
• Financial modeling
• Signal processing
• Physics equations

Mathematical Formula

For those interested, the hyperbolic sine is defined as:

SINH(x) = (e^x - e^-x) / 2

where e is Euler’s number (approximately 2.71828).