For some values of x, cos x has value 0. For example, x = π/2 and x = 3π/2. When this happens, we have 0 in the denominator of the fraction and this means it is undefined. So there will be a "gap" in the function at that point. This gap is called a discontinuity.

y = tan x.

we know that tan x is a periodic function with period

The graph of y = tan x is

Note that there are vertical asymptotes (the blue dotted lines) where the denominator of tan x has value zero.

____________________________________________________________________________

As there is a phase shift in the sine and cosine graph, in the same way there is a phase shift in tangent graph. y = a tan (bx + c) bx + c = 0 ⇒ x = -c/b that is the first cycle. Period = π/|b| For every cycle add k(π/|b|) that gives you the asymptotes. Example: y = 4tan(2x + π/3) 2x + π/3 = 0 ⇒ x =-π/6 Period = π/b = π/2

Phase shift = -π/6 = -4π/24

Add and subtract π/6

It will be -π/24 and -7π/24

___________________________________________________________________

1) Find the period of y = tan (3x)

The general equation of tangent function is

y = a tan(bx)

a = 1 Period = π/b

Period = π/3

__________________________________________________________________________

2) y = 3 tan(2x)

The general equation of tangent function is

y = a tan(bx)

a = 3 and b = 2

Period = π/b

∴ Period = π/2

________________________________________________________________

1) Draw the graph of y = tan 2x.

2) From the given graph write the function of it.

Graph Dictionary

Home Page

GMAT

GRE

1st Grade

2nd Grade

3rd Grade

4th Grade

5th Grade

6th Grade

7th grade math

8th grade math

9th grade math

10th grade math

11th grade math

12th grade math

Precalculus

Worksheets

Chapter wise Test

MCQ's

Math Dictionary

Graph Dictionary

Multiplicative tables

Math Teasers

NTSE

Chinese Numbers

CBSE Sample Papers