This graph is also discontinuous graph because we know that

Cot x = cos x / sin x

For some values of x, sin x has 0 value.

For example,

for these values the denominator becomes zero and the cot x is undefined at these particular value. So there is a gap and discontinuity.

The periodic function of cot x is π This means it repeats itself after each π as we go left to right on the graph.

So considering the values of cos x and sin x for different values of x we can sketch the graph of y = cot x as follows.

____________________________________________________________________

As there is a phase shift in the sine and cosine graph, in the same way there is a phase shift in cotangent graph.

y = a cot(bx + c)

bx + c = 0

⇒ x = -c/b which is the first cycle.

Period = π/|b|

For every cycle add k(π/|b|) that gives you the asymptotes.

4x - π/2 = 0

⇒ x = π/8

Period = π/b = π/8

As there is 4x so divide the cycle in 4 pieces of length and as there is negative sign, the phase shift is at left.

It will start from π/8 = 2π/16 and then add π/16 to each cycle.

It will end at π/8 + 4π/16= 6π/16.

So the graph will be between 2π/16 to 6π/16. So it will look like as follows :

________________________________________________________________________

a) Find the period.

b) Find the equation of vertical asymptote.

a) Find the period.

b) Phase shift.

c) Graph the given function.

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