# Arcsin Calculator

The online arcsin(x) (inverse sine) calculator is a tool that helps determine the angle in radians or degrees whose sine is equal to a given value. It allows you to find the angle measurement when you know the sine of that angle.

## What is Arcsine

Arcsine, also known as inverse sine, is a mathematical function that gives the angle whose sine is a given number or ratio. It is the inverse of the sine function. The arcsine function is denoted as arcsin(x) or asin(x), where x is the input value. For example, if you have a value of 0.5 and you want to find the corresponding angle, you would use the arcsine function. It will return the angle (in radians or degrees) whose sine is approximately 0.5. The arcsine function is commonly used in mathematics, physics, computer science, and engineering to solve problems involving angles, circles, and trigonometry.

## Arcsine definition

The arcsine function is the inverse function of y = sin(x).

arcsin(*y*) = sin^{-1}(*y*) = *x* + 2*kπ *

For every

*k *= {...,-2,-1,0,1,2,...}

For example, If the sine of 30° is 0.5:

sin(30°) = 0.5

Then the arcsine of 0.5 is 30°:

arcsin(0.5) = sin^{-1}(0.5) = 30°

### Arcsine table

y | x = arcsin(y) | |
---|---|---|

degrees | radians | |

-1 | -90° | -π/2 |

-0.8660254 | -60° | -π/3 |

-0.7071068 | -45° | -π/4 |

-0.5 | -30° | -π/6 |

0 | 0° | 0 |

0.5 | 30° | π/6 |

0.7071068 | 45° | π/4 |

0.8660254 | 60° | π/3 |

1 | 90° | π/2 |

## Arcsin Calculator Example

Input (Sine Value) | Output (Arcsin Value) |
---|---|

0 | 0 radians / 0 degrees |

0.5 | 0.5236 radians / 30 degrees |

0.707 | 1.0472 radians / 60 degrees |

1 | 1.5708 radians / 90 degrees |

-0.5 | -0.5236 radians / -30 degrees |

-0.866 | -1.0472 radians / -60 degrees |

-1 | -1.5708 radians / -90 degrees |

In this example, you can input different values for the sine and obtain the corresponding arcsin values in both radians and degrees. This table provides a clear visualization of how the arcsin function calculates the angles based on the given sine values.

Please note that the values in the table are rounded to four decimal places for simplicity. Depending on your specific calculator or programming application, you may get more precise results.