arccosecant

9.9

An angle whose sine equals 1 divided by a given number

noun
/ˌɑrkəʊˈsiːkənt/

Specialized

: arcocosecante

In trigonometry, the arccosecant is used to determine the angle when the value of cosecant is known.

Examples

The arccosecant of 2 is approximately 30 degrees.
You can find the angle by taking the arccosecant of the number.
The arccosecant function is less common than arcsine or arccosine but is sometimes needed in advanced calculations.
To find the arccosecant, use the inverse cosecant function.
To find the angle corresponding to a cosecant value of 3, you can calculate the arccosecant of 3.
In calculus, the arccosecant helps in determining angles in trigonometric integrals.
When solving triangles, the arccosecant function is essential for finding angles based on cosecant values.

Synonyms

arc cosecant

vsarccosecant

Specialized

9.9

To give the angle in trigonometry whose cosecant equals a number

is the same meaning but written as one combined word

inverse cosecant

vsarccosecant

Specialized

9.9

An angle whose cosecant equals a given number

uses a shorter combined word form rather than the longer phrasing

Surface Forms

arccosecant singular

arccosecants plural

Morphology

arccosecant = cosecant (semi-transparent) = arc + cosecant

The prefix 'arc' indicates an inverse trigonometric function, but this may not be immediately clear to all learners.

Etymology

Arccosecant joins arc 'a part of a circle' and cosecant, which has co- and secant and is related to the familiar word section 'to cut or divide'. So arccosecant is the angle, the arc you get when you undo the cosecant, and it gives the angle whose cosecant is a given number.