What is the period of the f(x)=\sin x+\sin 3x? f(x)=\sin x+\sin

lunnatican4

lunnatican4

Answered question

2022-01-15

What is the period of the f(x)=sinx+sin3x?
f(x)=sinx+sin3x=23x+x2cosx3x2=2sin2xcosx=4sinxcos2x
f(x+T)=4sin(x+T)cos2(x+T)=4sinxcos2x

Answer & Explanation

mauricio0815sh

mauricio0815sh

Beginner2022-01-16Added 34 answers

In general, if T is the period of a function f(x) then the period of the function f(ax) is Ta.
Suppose two periodic functions f1(x)  and  f2(x) have periods T1 and T2. Then the period of the function g(x)=f1(x)±f2(x) is LCM (least common multiple) of T1  and  T2 (although, this certainly isn't true for all periodic functions, as explained inside this answer.)
In your question the periods of sinx and sin3x are calculated as 2π1=2π and 2π3 respectively.
So the period of the function f(x)=sinx+sin3x is the LCM (2π,2π3)=2π.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?