Determining the period of a trigonometric function

[ainster31]

Homework Statement

$$f(x)=sin2x+cos4x$$

Homework Equations

The Attempt at a Solution

$$The\quad period\quad of\quad sin2x\quad is\quad π.\quad The\quad period\quad of\quad cos4x\quad is\quad \frac { π }{ 2 } .\\ \\ What\quad is\quad the\quad period\quad of\quad f(x)?$$

 

[Tanya Sharma]

Homework Statement

$$f(x)=sin2x+cos4x$$

Homework Equations

The Attempt at a Solution

$$The\quad period\quad of\quad sin2x\quad is\quad π.\quad The\quad period\quad of\quad cos4x\quad is\quad \frac { π }{ 2 } .\\ \\ What\quad is\quad the\quad period\quad of\quad f(x)?$$

What is the lowest common multiple of the periods of sin2x and cos4x ?

 

[arildno]

Suppose you have two periods, p_1 and p_2
the COMMON period must then satisfy n*p_1=m*p_2, for integers n and m to be determined.

That is, the common period must be, as Tanya Sharma says, a COMMON MULTIPLE of the two periods, and the LEAST one at that.

 

[ainster31]

How does that work considering that cos is sin but displaced on the x-axis?

According to this graph, T=pi is wrong:

 

[ainster31]

Never mind.

I'm an idiot. You're right.

Thanks.

 

[arildno]

No,it isn't.

Look at the respective function values of sin(2x) and cos(4x) at two x's a pi apart.

BOTH functions repeat THEMSELVES here, whether you use -pi/3 and 2pi/3 or "0 and pi" or whatever other couple of x's.

The common period of two functions does NOT mean that they equal each other at those points.