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. In the example in cell A4, the result is converted from radians, into degrees.

The formulas are shown in the spreadsheet on the left and the results are shown in the spreadsheet on the right.

 Formulas:
  A
1 =ASIN( -1 )
2 =ASIN( 0 )
3 =ASIN( 1 / SQRT(2) )
4 =DEGREES( ASIN( 1 / SQRT(2) ) )
 Results:
  A B
1 -1.570796327 - Result is -π/2 radians
2 0 - Result is 0 radians
3 0.785398163 - Result is π/4 radians
4 45 - Result is 45 degrees

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


Excel Asin Function Common Error

If you get an error from the Excel Asin Function, this is likely to be the #NUM! error:

Common Error
#NUM! - Occurs if the supplied number argument is not in the range -1 to +1.
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