Arccosine is a mathematical term that is commonly used in trigonometry. It is the inverse function of cosine, which means that it is used to find the angle whose cosine is a given number. In this article, we will explore the definition and meaning of arccosine, its origin, and its associations.
Definitions
Arccosine is defined as the inverse cosine function. It is denoted by arccos(x) or cos^-1(x). The function takes a value between -1 and 1 as input and returns an angle between 0 and pi radians as output. The arccosine of a number x is the angle whose cosine is x.
Origin
The term arccosine comes from the Latin word “arcus,” which means “arc” or “curve,” and “cosine,” which is a trigonometric function. The concept of inverse trigonometric functions was first introduced by the French mathematician Jean-Robert Argand in the early 19th century.
Meaning in different dictionaries
According to the Merriam-Webster dictionary, arccosine is “the inverse function of the cosine function when restricted to an interval for which the cosine is one-to-one and which contains the range of the cosine function.” The Oxford English Dictionary defines it as “the angle whose cosine is a given number.”
Associations
Arccosine is closely related to other trigonometric functions, such as sine, cosine, and tangent. It is used in various mathematical applications, such as calculating the angles of triangles and solving equations involving trigonometric functions.
Synonyms
The synonyms of arccosine include inverse cosine, cos^-1, and arc cosine.
Antonyms
There are no antonyms of arccosine as it is a mathematical term and does not have an opposite.
The same root words
Arccosine shares the same root words with other trigonometric functions, such as arcsine and arctangent.
Example Sentences
- To find the angle whose cosine is 0.5, we need to use the arccosine function.
- The arccosine of 1 is 0 degrees.
- The arccosine of -0.5 is approximately 120 degrees.
- The arccosine function is used to solve equations involving cosine.