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°

Solved Examples

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°

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