The arc cosine of a number x is a real number for which the cosine is x.
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) = 360n ± 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°.”