Properties of Tangent Function

Next, let us go through some of the important properties of the tangent function. The basic properties of tan x along with its value at specific angles and the trigonometric identities involving tan x are:

• The tangent function is an odd function because tan (-x) = -tan x.
• Tan x is not defined at values of x where cos x = 0.
• The graph of tan x has an infinite number of vertical asymptotes.
• The values of the tangent function at specific angles are:
  • tan 0 = 0
  • tan π/6 = 1/√3
  • tan π/4 = 1
  • tan π/3 = √3
  • tan π/2 = Not defined
• The trigonometric identities involving the tangent function are:
  • 1 + tan²x = sec²x
  • tan 2x = 2 tan x/(1 – tan²x)
  • tan (a – b) = (tan a – tan b)/(1 + tan a tan b)
  • tan (a + b) = (tan a + tan b)/(1 – tan a tan b)
• The graph of tan x is symmetric with respect to the origin.
• The x-intercepts of tan x are where sin x takes the value zero, that is, when x = nπ, where n is an integer.

Important Notes on Tangent Function:

• The tangent function is expressed as tan x = sin x/cos x and tan x = Perpendicular/Base
• The slope of a straight line is the tangent of the angle made by the line with the positive x-axis.