# Arc Cosecant

## Arc Cosecant

The arc cosecant of a number x is a real number for which the cosecant is x.

In a trigonometric context, the cosecant of an angle A is the multiplicative inverse of the sine ratio of angle A. The cosecant relationship of an angle x is a function, but the inverse relationship defined by y = arccsc(x) is not a function.

### Notation

The symbol for the arc cosecant relationship of the number x is “arccsc(x)” which is read as “arc cosecant of x.”

### Examples

In the sexagesimal system of measuring angles, we have:

• arccsc(2) = 30
• arccsc(2) = 180n ± 30, where n is an integer.

Because csc(30°) = 2. The same is true for all angles of “30° ± a multiple of 180°.”