# Documentation/Calc Functions/ACOS

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ACOS

Mathematical

## Summary:

Calculates the inverse trigonometric cosine (arccosine or arccos) of a real number. The value returned is the principal value and lies in the range [0,π] radians.

ACOS(Number)

## Returns:

Returns a real number in the range [0,π] that is the inverse trigonometric cosine 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 cosine is to be calculated.

• If Number is non-numeric, then ACOS reports a #VALUE! error.
• If Number lies outside the range [-1, 1], then ACOS 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 cosine of x is:

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

The figure below illustrates the function ACOS.

## Examples:

Formula Description Returns
=ACOS(-1) Inverse trigonometric cosine of -1. 3.14159265358979 (π)
=ACOS(D1) where cell D1 contains the number 0.5. Inverse trigonometric cosine of 0.5. 1.0471975511966 (π/3)
=DEGREES(ACOS(0.5)) Inverse trigonometric cosine of 0.5, converted to degrees. 60
=ACOS(-0.5)*180/PI() Inverse trigonometric cosine of -0.5, converted to degrees. 120
=DEGREES(ACOS(COS(RADIANS(60))) An angle of 60° is converted to radians, its cosine is taken, then the inverse cosine of that value is calculated, and finally the result is converted back to degrees. 60

ACOS