# Documentation/Calc Functions/ASIN

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ASIN

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.

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.

• 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:

$\displaystyle{ \arcsin(x) ~=~ \sum_{n=0}^{\infty } \left ( \frac{(2n)!}{2^{2n}(n!)^2(2n+1)} \right )x^{2n+1} }$

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

ASIN