Determining the period of a trigonometric function

  • Thread starter ainster31
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  • #1
ainster31
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Homework Statement



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

Homework Equations




The Attempt at a Solution



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

Answers and Replies

  • #2
Tanya Sharma
1,540
135

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 ?
 
  • #3
arildno
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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. :smile:
 
  • #4
ainster31
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How does that work considering that cos is sin but displaced on the x-axis?

According to this graph, T=pi is wrong:

eZclCyl.png
 
  • #5
ainster31
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Never mind.

I'm an idiot. You're right.

Thanks.
 
  • #6
arildno
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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.
 

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