Tangent Function

In this page we are going discuss about trigonometry tangent function .The trigonometry tangent is one of the interesting topics in mathematics. It can be generally used in trigonometry. Trigonometry tangent function represents the ratio of sides of the triangle. It is known as circular function. Since their values can be the ratios of x and y co-ordinates on a circle of radius 1. Tangent is a one of the type of trigonometric functions. 

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Tangent function formulas

• Tangent of an angle is the ratio of length of the adjacent and the opposite side.
  tan x = `(opposite)/(adjacent)`
• The tangent is the inverse of the cotangent and is given by
  tan x = `(1)/(cot x)` 
•  Quotient of sine and cosine functions is called as tan or tangent function.
  tan x = `(sin x)/(cosx)`

Properties

Below are the propertise of tangent function -

• The tangent is an odd function.
          tan (−x) = −tan x
• The graph of a tangent function is symmetric with the origin (0, 0).
• The period of the cotangent function is `pi`.
• The tangent function is undefined on the interval (0,`pi` ) and thus has a vertical asymptotic at x = `pi`.
• The domain of the tangent function is all the real numbers except ( `pi`/2 + k`pi` )
• The range of the tangent function is (−`oo` , +`oo`)
• Co-function for tangent

a relation between the tangent and cotangent both are the co-function of the other.
cot A = tan (90° - x)

Graph for Tangent function:
              y = f (x) = tan x
             

Examples

Below are the examples on tangent function -
Example 1:
Find the function value of tan 60^o.
Solution: Use the tangent's co function identity to solve the problem.
tan x = cot (90^o – x)
tan 60^o = cot (90^o – 60^o)
= cot (30^o)
tan 60^o = 1.732
The tangent of 60^o is 1.732

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Example 2: 
Find the function value of tan 25^o.
Solution: Use the tangent's co function identity to solve the problem.
tan x = cot(90^o – x)
tan 25^o = cot (90^o – 25^o )
= cot (65^o)
tan 25^o = 0.4663
The tangent of 25^o is 0.4663