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# Arccot Formula

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:

\(θ = \text{arccot} \left(\dfrac{\text{adjacent}}{\text{opposite}}\right) \)

The graph of Arccot is shown below:

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## 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,

\(θ = \text{arccot} \left(\dfrac{\text{adjacent}}{\text{opposite}}\right) \)

\( θ = \text{arccot} \left( \dfrac{34}{22}\right) = 32.998^\circ \)

**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,

\(θ = \text{arccot} \left(\dfrac{\text{adjacent}}{\text{opposite}}\right) \)

\( θ = \text{arccot} \left(\dfrac{4}{3}\right) = 36.877^\circ \)

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

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