Inverse Tangent Formula

In trigonometry, every function has an inverse and so is tangent. This operation inverses the function so the tangent becomes inverse tangent through this operation. Then the inverse tangent is used to find the degree value of an 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 Tangent is also called as arctan or tan-1

The arctan Formula is:

Tangent = Opposite / Adjacent

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

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

Solved Examples

Example 1: From the given figure, find the value of x.

Inverse tangent formula example

From the given,
AB = 3 cm, BC = 4 cm
tan x = AB/BC
tan x = ¾ = 0.75
x = tan-1(0.75)
x = 36.9°

Example 2: If sin x = 0 and cos x = 1, then find the tan-1x.
sin x = 0
x = sin-1(0) = 0
cos x = 1
x = cos-1(1) = 0
tan-1x = tan-1(0) = 0

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