Arc secant is a mathematical term that is used to describe a function that is the inverse of the cosine function. It is an important concept in trigonometry and is used in many different fields of mathematics and science. In this article, we will explore the definition and meaning of arc secant, its origin, and its associations.

## Definitions

Arc secant is defined as the inverse of the cosine function. It is denoted by sec^-1(x) or arcsec(x), where x is the value of the cosine function. The arc secant of x is the angle whose cosine is x. In other words, if cos(y) = x, then arcsec(x) = y.

## Origin

The term arc secant comes from the Latin word “secare,” which means “to cut.” The term was first used by the Greek mathematician Hipparchus in the second century BC. He used the term to describe a line that cuts a circle or a sphere in two places.

## Meaning in different dictionaries

According to the Oxford English Dictionary, arc secant is defined as “the inverse of the cosine function.” The Merriam-Webster Dictionary defines it as “the angle whose secant is a given number.”

## Associations

Arc secant is closely related to other trigonometric functions such as sine, cosine, tangent, and cotangent. It is also used in calculus, geometry, and physics.

## Synonyms

The synonyms of arc secant include inverse cosine, arc cos, and arccosine.

## Antonyms

There are no antonyms of arc secant.

## The same root words

The same root words of arc secant include secant, cosine, and trigonometry.

## Example Sentences

- The arc secant of 0.5 is 60 degrees.
- To find the angle whose cosine is 0.8, we need to use the arc secant function.
- The arc secant function is used to solve many different types of problems in mathematics and science.