Trigonometry

Arc Cosine

The arc cosine of a number x is a real number for which the cosine is x.
arccos
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 “[latex]cos^{-1}[/latex]” (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°) = [latex]\frac{1}{2}[/latex], arccos(0.5) = 60°. The same is true for all angles of “60° ± 360°.”

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