Arc Cosine

Arc Cosine

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°.”