# Online Arctan Calculator

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# Arctan Calculator

For example, If the tangent of 45° is 1:

tan(45°) = 1

Then the arctangent of 1 is 45°:

arctan(1) = tan^{-1}(1) = 45°

## Arctangent table

y | x = arctan(y) | |
---|---|---|

degrees | radians | |

-1.732050808 | -60° | -π/3 |

-1 | -45° | -π/4 |

-0.577350269 | -30° | -π/6 |

0 | 0° | 0 |

0.577350269 | 30° | π/6 |

1 | 45° | π/4 |

1.732050808 | 60° | π/3 |

Here we discuss list of online math calculators that help us for doing calculation easily.

### Arctan Calculator

The arctan is the inverse of the tangent. It is normally represented by arctan(θ) or tan^{-1}(θ).Use arctan calculator to easily calculate the arctan of a given number. Online arctangent calculation tool to compute the arcus tangens function in degrees or radians. Supports input of decimal numbers (0.5, 6, -1, etc.) and fractions (1/3, 3/4, 1/6, -4/3 etc.).

** Arctangent definition**

The arctangent function is the inverse function of y = tan(x).

arctan(y) = tan^{-1}(y) = x+ kπ

For every

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

For example, If the tangent of 45° is 1:

tan(45°) = 1

Then the arctangent of 1 is 45°:

arctan(1) = tan^{-1}(1) = 45°

** How to Use the Arctan Calculator?**

The procedure to use the arctan calculator is as follows:

1. Enter the tangent value in the respective input field

2. Now click the button “Calculate Arctan” to get the angle

3. Finally, the angle in both degree and radian measure will be displayed in the output field

** What is arctan?**

Arctangent is the inverse of the tangent function. Simply speaking, we use arctan when we want to find an angle for which we know the tangent value.

However, in the strictest sense, because the tangent is a periodic trigonometric function, it doesn't have an inverse function. Still, we can define an inverse function if we restrict the domain to the interval where the function is monotonic. Using the tan^{-1}x convention may lead to confusion about the difference between arctangent and cotangent. It turns out that arctan and cot are really separate things:

1. cot(x) = 1/tan(x), so cotangent is basically the reciprocal of a tangent, or, in other words, the multiplicative inverse

2. arctan(x) is the angle whose tangent is x

We hope that now you do not doubt that arctan and cotan are different. To avoid any further misunderstandings, you may want to use the arctan(x) rather than tan^{-1}x notation

** Arctan function :- **The arctan (a.k.a. arcus tangens) is one of the inverse trigonometric functions (antitrigonometric functions) and is the inverse of the tangent function. It is sometimes written as tan^{-1}(x), but this notation should be avoided as it can cause confusion with an exponent notation. The arctan is used to obtain an angle from the tangent trigonometric ratio, which is the ratio between the side opposite to the angle and the adjacent side of the triangle.

The function spans all real numbers (-∞ - +∞) and so do the results from our calculator. The range of the angle values is usually between -90° and 90°. There are a number of arctan rules, like that tan(arctan(x)) = x, or that arctanα + arctanβ = arctan((α + β) / (1-αβ)), as well as sine of the arctangent: sin(arctan(x)) = x / √(1+x^{2}), which can help you in trigonometry calculations.