Arccot Formula

Every function has an inverse and so is cotangent 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 have an inverse.

  • Sine
  • Cosine
  • Tangent
  • Secant
  • Cosecant
  • Cotangent

The inverse of these trigonometric functions are as follows:

  • inverse sine
  • inverse cosine
  • inverse tangent
  • inverse secant
  • inverse cosecant
  • inverse cotangent

The inverse of Cotangent is also called as arccot or Cot-1

The Formula for arccot is:

Cotangent = Base / Perpendicular

If in a triangle, Base to angle A is 1 and the perpendicular side is sqrt(3)

So cot-1 (1/sqrt 3) = A

= 600

Table values of arccot

The below table shows the values of arctan.

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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