The Excel ASIN Function

Arcsine

The Arcsine is the inverse of the sine.

Therefore, for the simple right-angled triangle below, the arcsine of the opposite side, o, divided by the hypotenuse, h, is equal to the angle θ.

Right-Angled Triangle

I.e. for the triangle above,

Arcsine Equation
The Inverse trig. functions are discussed further on the Wikipedia Inverse Trigonometric Functions Page

Basic Description

The Excel ASIN function calculates the arcsine (ie. the inverse sine) of a given number, and returns an angle, in radians, between -π/2 and π/2.

The syntax of the function is :

ASIN( number )

Where the number argument is the value, between -1 and +1, for which you want to calculate the arcsine.

Converting from Radians to Degrees

If you want the angle returned by the Asin function to be expressed in degrees, you can convert it, using the Excel Degrees function:

=DEGREES( radians )
An example of this is given below.

Excel Asin Function Examples

Column A of the spreadsheet below, shows examples of the Excel Asin Function, used to calculate the arcsine of different values.

 Formulas:
 A
1=ASIN( -1 )
2=ASIN( 0 )
3=ASIN( 1 / SQRT(2) )
4=DEGREES( ASIN( 1 / SQRT(2) ) )
 Results:
 AB
1-1.570796327 - Result is -π/2 radians
20 - Result is 0 radians
30.785398163 - Result is π/4 radians
445 - Result is 45 degrees

Note that in cell A4, the Excel Degrees function is used to convert the result from radians to degrees.


Further information and examples of the Excel Asin function can be found on the Microsoft Office website.


Asin Function Errors

If you get an error from the Excel Asin Function, this is likely to be one of the following:

Common Errors
#NUM!-Occurs if the supplied number argument is not in the range -1 to +1.
#VALUE!-Occurs if the supplied number argument is not recognised as a numeric value.