# Inverse Trigonometric functions

input sqrt(2) for square root of 2 for example.

## Table of inverse trigonometric functions in R (real numbers)

Function | Abbreviation | Domain | Range |
---|---|---|---|

Arcsine | y = Arcsin (x) | -1 <= x <= 1 | -π/2 < y < π/2 |

Arccosine | y = Arccos (x) | -1 <= x <= 1 | 0 <= y <= π |

Arctangente | y = Arctan (x) | all real numbers | -π/2 < y < π/2 |

Arccotangent | y = Arccot (x) | all real numbers | 0 < y < π |

Arcsecant | y = Arcsec (x) | x <= -1 or x >= 1 | 0 <= y < π/2 or π/2 < y <= π |

Arccosecant | y = Arccsc (x) | x <= -1 or x >= 1 | -π/2 <= y < 0 or 0 < y < π/2 |

## Arcsine

Arcsine function is the inverse function of the sine function. It gives the angle in radians knowing its sine value.

Arcsine domain of definition is [-1,1].

x= arcsin (y) `<=>`y = sin (x) and −π/2 < y <= π/2

## Arccosine

Arccosine function is the inverse function of the cosine function. It gives the angle in radians knowing its cosine value.

Its domain of definition is [-1,1].

x= arccosin (y) `<=>`y = cos (x) and 0 <= y <= π

## Arctangent

Arctangent function is the inverse function of the tangent function. It gives the angle in radians knowing the tangent value.

Its domain of definition is the set of real numbers.

x= arctan (y) `<=>`y = tan (x) and −π/2 <= y <= π/2

## Arccotangent

Arccotangent function is the inverse function of the cotangent function. It gives the angle in radians knowing the cotangent value.

Its domain of definition is the set of real numbers.

x= arccotan (y) `<=>`y = cotan (x) and 0 < y < π

## Arcsecant

Arcsecant function is the inverse function of the secant function. It gives the angle in radians knowing the secant value.

Its domain of definition is the set ] -∞, -1] U [1, +∞ [.

x= arcsec (y) `<=>`y = sec (x) and (0 < y < π/2 or π/2 < y < π)

## Arccosecant

Arccosecant function is the inverse function of the cosecant function. It gives the angle in radians knowing the cosecant value.

Its domain of definition is the set ] -∞, -1] U [1, +∞ [.

x= arccosec (y) `<=>`y = cosec (x) and (-π/2 < y < 0 or 0 < y < π/2)

## See also

Conversion of angle measurement

Trigonometric Functions