If T is the smallest positive real number such that f(x+T) = f(x) for all x, then T is called the fundamental period of f(x).

A pattern in which y -values repeats at regular interval. One such a complete pattern is called

Since sin(2nπ + θ) = sin θ, cos(2nπ + θ) = cos θ, for all values of θ and n $\epsilon$ N.

Therefore, sine and cosine functions are periodic functions.

We find that 2π is the smallest positive real number such that

sin (2π + θ) = sin θ and cos(2π + θ) = cos θ for all values of θ.

So sine and cosine function are periodic function with period 2π.

We also know that tan( π + θ ) = tan θ and cot ( π + θ ) = cot θ

Therefore tan θ and cot θ are periodic functions with period π.

Sine function : Period 2π
cosine function : Period 2π tangent function : Period π |
cosecant function : Period 2π secant function : Period 2π cotangent function : Period π |

So period of the given function is

3x = 2π

∴ x = $\frac{2π}{3}$

so the period of f(x) = $\frac{2π}{3}$

2) Find the period of the function f(x) = 3 sin (4x).

So period of the given function is

4x = 2π

∴ x = $\frac{π}{2}$

so the period of f(x) = $\frac{π}{2}$

3) Find the period of the function f(x) = -2 cos$\frac{θ}{6}$ .

So period of the given function is

$\frac{θ}{6}$ = 2π

∴ θ = 12π

From Periodic function in trigonometry to Home

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.

Russia-Ukraine crisis update - 3rd Mar 2022

The UN General assembly voted at an emergency session to demand an immediate halt to Moscow's attack on Ukraine and withdrawal of Russian troops.

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