Python Matplotlib #02 - Line Chart ...
Python Matplotlib #02 - Line Chart ( gráfico de linha )

Cotangent Graph

We at ask-math believe that educational material should be free for everyone. Please use the content of this website for in-depth understanding of the concepts. Additionally, we have created and posted videos on our youtube.

We also offer One to One / Group Tutoring sessions / Homework help for Mathematics from Grade 4th to 12th for algebra, geometry, trigonometry, pre-calculus, and calculus for US, UK, Europe, South east Asia and UAE students.

Affiliations with Schools & Educational institutions are also welcome.

Please reach out to us on [email protected] / Whatsapp +919998367796 / Skype id: anitagovilkar.abhijit

We will be happy to post videos as per your requirements also. Do write to us.

Cotangent graph is opposite to that of tangent graph.
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, x = ..., -3π, -2π, -π, 0, π, 2π, 3π, 4π, 5π, ...
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.



Note that there are vertical asymptotes (the blue dotted lines) where the denominator of cot 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 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.
Example: y = cot(4x - π/2)
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 :

________________________________________________________________________
Practice

1) y = cot(2x).
a) Find the period.
b) Find the equation of vertical asymptote.
2) y = cot(3x - π/2)
a) Find the period.
b) Phase shift.
c) Graph the given function.
Cotangent graph

Graph Dictionary

Home Page