SQL - ASIN() Function

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The SQL ASIN() function calculates the arc sine of a numeric value. This function accepts a single numeric value as an argument. The domain of the argument must be [-1,1] and the range of the result will be [-π/2, π/2]. If the value passed to this function doesn't lie in the given domain, it raises an error.

An arc sine of an angle is defined as the inverse of the sine function. A sine function is defined in a right-angled triangle as the ratio of an opposite side of a non-right angle to the hypotenuse. Therefore, the domain of the sine function will become the range of the arc sine function and vice-versa.

Syntax

Following is the syntax of SQL ASIN() function −

ASIN(number)

where, number is the value for which we need to calculate the arc sine.

Example

If we pass a positive value as an argument, then this function returns it's equivalent arc sine value which is positive as shown below −

SELECT ASIN(0.8)
AS Arcsine_Value

When we run above program, it produces following result −

+-------------------+
| Arcsine_Value     |
+-------------------+
| 0.927295218001612 |
+-------------------+

Example

If we pass a negative value as an argument to this function, then this function returns it's equivalent arc sine value which is negative as shown below −

SELECT ASIN(-0.5)
AS Arcsine_Value

While executing the above code we get the following output −

+--------------------+
| Arcsine_Value      |
+--------------------+
| -0.523598775598299 |
+--------------------+

Example

If the value passed to this function is not in the range of -1 to 1, then this function raises an error:

SELECT ASIN(6)
AS Arcsine_Value

Following is an output of the above code −

Msg 3623, Level 16, State 1, Line 1
An invalid floating point operation occurred.

Example

The arc sine value of 0 is 0.

SELECT ASIN(0)
AS Arcsine_Value

Output of the above code is as follows −

+-------------------+
| Arcsine_Value     |
+-------------------+
| 0                 |
+-------------------+

Example

When we calculate the arc sine value of a number and pass the result to the sin() function, the final result is equivalent to the original number.

SELECT ASIN(1)
AS Arcsine_Value

The result produced is as shown below −

+-------------------+
| Arcsine_Value     |
+-------------------+
| 1.5707963267949   |
+-------------------+

Now, we are trying to pass the value retrieved by the arc sine to the sin() function −

SELECT SIN(1.5707963267949)
AS sine_Value

The result obtained is as follows −

+------------+
| sine_Value |
+------------+
| 1          |
+------------+