The argument

*x*of the arc cosine relationship is always a real number between -1 and 1.The relation defined by *y* = arccos(*x*) is not a function.

### Notation

The symbol used for the arc cosine of a number *x* is “arccos(*x*)” which is read as “arc cosine of *x*.”

Some texts also use the notations “*Acos*” (European notation) or “\(cos^{-1}\)” (English notation) to indicate the arc cosine relationship. We can also find this notation on some calculators.

### Examples

In the sexagesimal system of measuring angles, we have:

- arccos(0,5) = 60
- arccos(0,5) = 360
*n*± 60 where*n*is an integer.

Because cos(60°) = \(\frac{1}{2}\), arccos(0.5) = 60°.

The same is true for all angles of “60° ± 360°.”