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Find the period of the function

  1. Apr 23, 2013 #1

    utkarshakash

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    1. The problem statement, all variables and given/known data
    Find period of the function
    f(x)=cos(cosx)+cos(sin x)

    2. Relevant equations

    3. The attempt at a solution
    the period of cosx=sinx=2∏. But here cosx and sinx are itself arguments to cosine function.
     
  2. jcsd
  3. Apr 23, 2013 #2

    Dick

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    Ok, then f(x)=f(x+2pi) is definitely true. You just have to figure out is there are any shorter periods. Sketching a graph will help.
     
  4. Apr 24, 2013 #3

    utkarshakash

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    OK so how do you graph these kinds of functions manually?
     
  5. Apr 24, 2013 #4

    ehild

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    Hint: Plot the function for multiples of pi/4.

    ehild
     
    Last edited: Apr 24, 2013
  6. Apr 25, 2013 #5

    utkarshakash

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    Ok I plotted functions cos(cosx) and cos(sinx) separately for multiples of pi/4 and got the respectives periods as pi. But the given function is sum of both functions. So I took the LCM of periods of both functions which comes out to be pi. But the correct answer is pi/2.
     
  7. Apr 25, 2013 #6

    ehild

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    Plot the whole function.
    It stays the same if the terms are interchanged. What are cos(cos(x+pi/2)) and cos(sin(x+pi/2)) equal to? Expand the arguments.

    ehild
     

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    Last edited: Apr 25, 2013
  8. Apr 25, 2013 #7

    vela

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    You might also find the identity
    $$\cos a + \cos b = 2\cos\left(\frac{a+b}{2}\right) \cos\left(\frac{a-b}{2}\right)$$ useful.
     
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