Arctan is a mathematical function that is used to determine the angle whose tangent is equal to a given number. It is also known as the inverse tangent function and is represented by the symbol tan⁻¹. In this article, we will explore the definition, origin, and meaning of arctan, as well as its associations, synonyms, and antonyms.
Definitions
Arctan is defined as the inverse of the tangent function. It is used to determine the angle whose tangent is equal to a given number. For example, if the tangent of an angle is 0.5, then the arctan of 0.5 is the angle whose tangent is 0.5.
Origin
The word arctan is derived from the Latin word “arcus” which means “arc” or “bow” and the word “tangens” which means “touching”. The term was first used in the 18th century by mathematicians who were studying the properties of trigonometric functions.
Meaning in different dictionaries
According to the Oxford English Dictionary, arctan is “the inverse of the tangent function”. The Merriam-Webster Dictionary defines it as “the angle whose tangent is a given number”. The Cambridge Dictionary defines it as “the angle whose tangent is a given number, measured in radians”.
Associations
Arctan is associated with trigonometry, which is the branch of mathematics that deals with the relationships between the sides and angles of triangles. It is also associated with calculus, which is the branch of mathematics that deals with the study of functions and their properties.
Synonyms
The synonyms of arctan include inverse tangent, atan, and tan⁻¹.
Antonyms
There are no antonyms of arctan as it is a mathematical function.
The same root words
The same root words as arctan include arc, tangent, and inverse.
Example Sentences
- To find the angle whose tangent is 0.5, you need to use the arctan function.
- The arctan of 1 is 45 degrees.
- The arctan of 0 is 0 degrees.
- The arctan of infinity is 90 degrees.
- The arctan function is used in many applications, including engineering, physics, and computer science.