Documentation/Calc Functions/ASIN
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Function name:
ASIN
Category:
Mathematical
Summary:
Calculates the inverse trigonometric sine (arcsine or arcsin) of a real number. The value returned is the principal value and lies in the range [-π/2, π/2] radians.
Syntax:
ASIN(Number)
Returns:
Returns a real number in the range [-π/2, π/2] that is the inverse trigonometric sine of Number in radians.
Arguments:
Number is a real number in the range [-1, 1], or a reference to a cell containing that number, whose inverse trigonometric sine is to be calculated.
- If Number is non-numeric, then ASIN reports a #VALUE! error.
- If Number lies outside the range [-1, 1], then ASIN reports a #NUM! error.
Additional details:
- To return the angle in degrees, use the DEGREES function.
- Alternatively multiply by 180/PI() to convert the result from radians to degrees.
The formula for the inverse trigonometric sine of x is:
[math]\displaystyle{ \arcsin(x) ~=~ \sum_{n=0}^{\infty } \left ( \frac{(2n)!}{2^{2n}(n!)^2(2n+1)} \right )x^{2n+1} }[/math]
The figure below illustrates the function ASIN.
Examples:
| Formula | Description | Returns |
|---|---|---|
| =ASIN(−1) | Inverse trigonometric sine of -1. | −1.5707963267949 (-π/2) |
| =ASIN(D1) where cell D1 contains the number 0.5. | Inverse trigonometric sine of 0.5. | 0.523598775598299 (π/6) |
| =DEGREES(ASIN(0.5)) | Inverse trigonometric sine of 0.5, converted to degrees. | 30 |
| =ASIN(−0.5)*180/PI() | Inverse trigonometric sine of -0.5, converted to degrees. | −30 |
| =DEGREES(ASIN(SIN(RADIANS(60))) | An angle of 60° is converted to radians, its sine is taken, then the inverse sine of that value is calculated, and finally the result is converted back to degrees. | 60 |
Related LibreOffice functions:
ODF standard:
Related (or similar) Excel functions:
ASIN