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.


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.


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°.”

Try Buzzmath activities for free

and see how the platform can help you.