The Excel ASIN Function
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.
I.e. for the triangle above,
The Inverse trig. functions are discussed further on the Wikipedia Inverse Trigonometric Functions Page
The Excel ASIN function calculates the arcsine (i.e. 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 provided below.
Excel Asin Function Examples
In column A of the following spreadsheet, the Excel Asin Function is used to calculate the arcsine of four different values.
|1||=ASIN( -1 )|
|2||=ASIN( 0 )|
|3||=ASIN( 1 / SQRT(2) )|
|4||=DEGREES( ASIN( 1 / SQRT(2) ) )|
|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|
Note that in cell A4, the Excel Degrees function is used to convert the calculated angle 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:
|#NUM!||-||Occurs if the supplied number argument is not in the range -1 to +1.|
|#VALUE!||-||Occurs if the supplied number argument is non-numeric.|