# Arc sine function

From Calculus

This article is about a particular function from a subset of the real numbers to the real numbers. Information about the function, including its domain, range, and key data relating to graphing, differentiation, and integration, is presented in the article.Template:Angular function convention

View a complete list of particular functions on this wiki

## Definition

The **arc sine** function is denoted or .

For in the closed interval (i.e., ), is defined as the unique value in the closed interval such that .

The arc sine function can be considered the inverse function of the restriction of the sine function to the interval .

## Key data

Item | Value |
---|---|

default domain | the closed interval |

range | the closed interval |

first derivative | , defined on the open interval . The left-hand derivative at 1 is not defined (as an infinity, it takes the value ). The right-hand derivative at -1 is not defined (as an infinity, it takes the value ). |