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Arccot formula is used in trigonometry, where the cotangent is defined as the ratio of the adjacent side to the opposite side of a specific angle of a right-angled triangle whereas arccot is the inverse of the cotangent function. Arccot is also known as cot^{-1}. The arccot formula is explained along with the solved examples below.

## What is Arccot Formula?

The basic arccot formula can be written as:

The graph of Arccot is shown below:

## Arccot Formula

Every function has an inverse in the trigonometry. This operation inverses the function, so the cotangent becomes inverse cotangent through this method. Then, the inverse cotangent is used to evaluate the degree value of the angle in the triangle(right-angled) when the sides opposite to and adjacent to the angles are known.

So each trigonometric function has an inverse. Below are the six trigonometric functions.

- Sine
- Cosine
- Tangent
- Secant
- Cosecant
- Cotangent

The inverse of these trigonometric functions are as follows:

- inverse sine (or) arcsine
- inverse cosine (or) arccos
- inverse tangent (or) arctan
- inverse secant (or) arcsec
- inverse cosecant (or) arccsc
- inverse cotangent (or) arccot

The inverse of Cotangent is also denoted as arccot or Cot^{-1}.

## The Formula for arccot is:

Cotangent = Base / Perpendicular |

If in a triangle, the base of the angle A is 1 and the perpendicular side is √3.

So, cot^{-1 }(1/√3) = A

cot A = 1/√3

cot A = cot 60°

A = 60°

## Table values of arccot

The below table shows the values of arccot.

x | arccot(x) | arccot(x) |

-√3 | 5π/6 | 150° |

-1 | 3π/4 | 135° |

-√3/3 | 2π/3 | 120° |

0 | π/2 | 90° |

√3/3 | π/3 | 60° |

1 | π/4 | 45° |

√3 | π/6 | 30° |

## Examples Using Arccot Formula

**Example 1: **In the right-angled triangle DEF, if the base of the triangle is 34 and the height is 22. Find the base angle.

**Solution:**

To find: θ

Using the arccot formula,

**Answer:** Therefore, θ = 32.998^{o}.

**Example 2: **In the right-angled triangle XYZ, if the base of the triangle is 4 and the height is 3. Find the base angle.

**Solution:**

To find: θ

Using the arccot formula,

**Answer:** Hence, the value of c is 1.

**Example 1: If x = cot ^{-1}(-√3/3), then what is the value of x?**

Solution:

Given,

x = cot^{-1}(-√3/3)

We know that cot 2π/3 = -√3/3

x = cot^{-1}(cot 2π/3)

Therefore, x = 2π/3 or x = 120°

**Example 2: Find the value of A if A = cot ^{-1}(-1).**

Solution:

Given,

A = cot^{-1}(-1)

We know that cot 3π/4 = -1

A = cot^{-1}(cot 3π/4)

Therefore, A = 3π/4 = 135°

**Example:**

In a given triangle, the base of the angle C is 1 and the perpendicular side is √3.

So, cot^{-1} (1/√3) = C

cot C = 1/√3

cot C = cot 60°

C = 60°

## Arccot Formula FAQs

**What is arccot equal to?**

Denotes an inverse function, not the multiplicative inverse. The principal value of the inverse cotangent is implemented in the Wolfram Language as ArcCot[z]. This definition is also consistent, as it must be, with the Wolfram Language’s definition of ArcTan, so ArcCot[z] is equal to **ArcTan[1/z]**.

**What is arccot simplified?**

The arccot function, denoted as **arccot(x) or cot(−1)(x)**, is the inverse function of the cotangent function. It takes a value x as its input and returns the angle whose cotangent equals x. Essentially, it allows us to find the angle when we know the cotangent value.

**Is arccot the same as cot 1?**

Arccot is also referred to as cot^{–}^{1}. Example: In a given triangle, the base of the angle C is 1 and the perpendicular side is √3.

**Is there an arccot?**

The six important trigonometric ratios are sine, cosine, tangent, cosecant, secant and cotangent. The inverse of these functions is called the inverse trigonometric function. The inverse of the cotangent function is called inverse cotangent or arccot.

**What is the value of arccot (- 1?**

The exact value of arccot(−1) is 3π4 3 π 4 . The result can be shown in multiple forms.

**What is the inverse of arccot?**

Mathematically, it is written as cot^{-1}x or arccot x, pronounced as ‘cot inverse x’ and ‘ arc cot x’, respectively. If a function f is invertible and its inverse is f^{-1}, then we have f(x) = y ⇒ x = f^{-1}(y). Therefore, we can have cot inverse x, if x = cot y, then we have y = cot^{-1}x.

**What is arccot radical 3?**

The exact value of arccot(√3) is **π6** .

**What is arccot 0 in terms of pi?**

The exact value of arccot(0) is **π2** . The result can be shown in multiple forms.

**Is arccos and cos 1 the same?**

**cos ^{−1}y = cos^{−1}(y), sometimes interpreted as arccos(y) or arccosine of y**, the compositional inverse of the trigonometric function cosine (see below for ambiguity)

**Can arccos be negative?**

The ArcCosine (or Inverse Cosine) of a number is an ANGLE. Can an angle be negative? Of course it can: if CCW is defined as a positive rotational direction, then a CW angular rotation will be negative.

**Are Arcsin and arccos the same?**

What is the difference between Arcsin and Arccos? Arcsin is used to find the measure of the angle opposite the given leg length in a right triangle. Arccos is used to find the measure of the angle adjacent to the given leg in a right triangle.

**Can arccos be undefined?**

Like any functions, they take a number as input and output a number. Of course, while the domain of cosine is all real numbers, the range is from -1 to 1 so the domain of arccosine is -1 to 1 and so **arccos(30) is undefined**.

**Where can arccos exist?**

The domain of arcos(x) is **−1 ≤ x ≤ 1** , the range of arcos(x) is [0 , π] , arcos(x) is the angle in [0, π] whose cosine is x. The domain of arctan(x) is all real numbers, the range of arctan is from −π/2 to π/2 radians exclusive .

**Is arccos even or odd?**

For odd function f(-x)= – f(x) so it is symmetrical about the origin. None of these 2 conditions hold for arccos (x) so it is neither.

**Is arccos the inverse?**

The arccos function is the inverse of the cosine function. It returns the angle whose cosine is a given number. Try this Drag any vertex of the triangle and see how the angle C is calculated using the arccos() function. Means: The angle whose cosine is 0.866 is 30 degrees.

**Why do we use arccos?**

Inverse cosine is also known as arccosine. It is the inverse of cos function. Also, sometimes abbreviated as ‘arccos’. It is used to measure the unknown angle when the length of two sides of the right triangle are known.

**How to calculate arccos?**

The arrcos function means the inverse of the cosine function. It is used to find the measure of an angle when the value of its cosine is known. The formula for arccos is c o s − 1 . The value of arccos can be found using a trigonometric value table if the cosine value is on the table.

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