Use this arcsine calculator to quickly calculate the arcsine the a number. Digital arcsine calculation tool through output in levels or radians. Support input of decimal numbers (0.5, 6, -1, etc.) and also fractions (1/4, 2/3, 4/3, 1/3 etc.).

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## Arcsine function

The arcsine is one of the station trigonometric functions (antitrigonometric functions) and also is the station of the sine function. That is occasionally written as sin-1(x), yet this notation must be avoided as it deserve to be confused with an exponent notation (power of, increased to the strength of). The arcsine is offered to acquire an angle from the sine trigonometric ratio, i m sorry is the ratio in between the next opposite to the angle and the longest side of the triangle.

The function spans from -1 to 1, and also so carry out the outcomes from ours arcsin calculator. The range of the angle values is usually in between -90° and also 90°. There room a variety of arcsin rules, prefer that sin(arcsin(x)) = x, or that arcsinα + arcsinβ = arcsin(α√(1-β2) + β√(1-α2)), and also cosine of the arcsine: cos(arcsin(x)) = sin(arccos(x)) = √(1-x2), which can aid you in trigonometry calculus.

## just how to calculation the arcsine the a number?

The easiest method to calculation it is by making use of our arcsin calculator above, which will certainly output outcomes in both degrees and also radians. Other ways encompass other given information, such together the worths of various other trigonometric features for the exact same angle or various other angles in the exact same triangle.

Here is a table of usual arcsin values:

Common values of the arcsin functionxarcsin(x) (°)arcsin(x) (rad.)-1 | -90° | -π/2 |

-√3 / 2 | -60° | -π/3 |

-√2 / 2 | -45° | -π/4 |

-1/2 | -30° | -π/6 |

0 | 0° | 0 |

1/2 | 30° | π/6 |

√2 / 2 | 45° | π/4 |

√3 / 2 | 60° | π/3 |

1 | 90° | π/2 |

π is, the course, the mathematical constant about equal to 3.14159.

## using arcsine to discover an angle

Given the ideal angled triangle in the figure below with recognized length of next a = 52 and of the hypotenuse c = 60 the inverse cosine function arcsin have the right to be supplied to find the angle α at suggest A.

First, calculation the sine of α through dividng the opposite side by the hypotenuse. This results in sin(α) = a / c = 52 / 60 = 0.8666. Usage the inverse role with this result to calculate the edge α = arcsin(0.8666) = 60° (1.05 radians).

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Cite this calculator & page

If you"d prefer to mention this virtual calculator source and info as provided on the page, you deserve to use the following citation: Georgiev G.Z., *"Arcsin Calculator"*,