Arc tangents are a mathematical concept that is widely used in trigonometry. The term ‘arc tangent’ is derived from the Latin word ‘arcus’, which means ‘bow’ or ‘arch’, and ‘tangens’, which means ‘touching’. In this article, we will discuss the definition, meaning, and various aspects of arc tangents.

## Definitions

Arc tangent is defined as the inverse function of the tangent. It is a function that maps the ratio of the opposite side of a right-angled triangle to the adjacent side to an angle. The arc tangent of a number is the angle whose tangent is equal to that number.

## Origin

The concept of arc tangent was first introduced by the Greek mathematician Hipparchus in the 2nd century BCE. He used the concept of arc tangent to calculate the position of the sun and the moon in the sky. Later, the concept was further developed by other mathematicians such as Ptolemy, Al-Khwarizmi, and Aryabhata.

## Meaning in different dictionaries

According to the Oxford English Dictionary, arc tangent is defined as “the angle whose tangent is a given number, or the value of this angle expressed in degrees or radians.” The Merriam-Webster Dictionary defines it as “the angle whose tangent is a given number.”

## Associations

Arc tangents are associated with various trigonometric functions such as sine, cosine, and tangent. They are also used in various fields such as physics, engineering, and astronomy to calculate angles and distances.

## Synonyms

The synonyms of arc tangent are inverse tangent, arctan, and atan.

## Antonyms

There are no direct antonyms of arc tangents as it is a mathematical concept.

## The same root words

The same root words of arc tangents are arc and tangent. The word ‘arc’ refers to a curved line, while ‘tangent’ refers to a straight line that touches a curve at a single point.

## Example Sentences

- The arc tangent of 1 is 45 degrees or pi/4 radians.
- To calculate the angle of elevation, we need to use the arc tangent function.
- The arc tangent of 0.5 is 26.57 degrees or 0.463 radians.
- The arc tangent of infinity is pi/2 radians or 90 degrees.
- The arc tangent function is used to calculate the phase angle in electrical circuits.