Arccot Formula


About Arccot Formula

In trigonometry, the arccot formula is the inverse of the cotangent function, which is defined as the ratio of the adjacent side to the opposite side at a certain angle of a right-angled triangle. Cot-1 is another name for Arccot. The Arccot formula is presented here, along with illustrations.

What is Arccot Formula?

The basic arcot formula will be written as:

θ = arccot(adjacent/opposite)

Examples Using Arccot Formula:

Example 1: In a 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 = arccot(adjacentopposite)θ = arccot(adjacentopposite)

θ = arccot(3422) = 32.998?θ = arccot(3422) = 32.998?

Answer: Therefore, θ = 32.998?.

Example 2: In a 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 = arccot(adjacent/opposite)

θ = arccot(43) = 36.877?

Thus, the value of c is 1.

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Frequently Asked Questions

The Arccot formula, also known as the inverse cotangent function, is defined as:
arccot(x)=tan⁡-1(1/x)
It gives the angle whose cotangent is x, typically measured in radians.

The arccot function can be rewritten using the arctan function as:
arccot(x)=π/2−tan⁡-1(x)
This identity helps in converting between inverse trigonometric functions for more straightforward calculations.

The arccot formula is widely used in geometry, physics, and engineering, especially in solving right-angle triangles, analyzing wave functions, and designing electronic circuits involving phase angles.