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  • is pi a period of
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  • Hi shashank
    pi is the first answer that comes to mind but it is not the answer.
    although the function repeats itself after every pi.
    But, by definition period is the smallest value for which the function repeats itself.
    To solve such questions , we can follow 2 approaches : Graphical and Numerical.
    This is a simple graph and can be done , but it is not always possible to draw graphs.
    So a more general solution :
    f(x + T ) = f(x)
    Case 1 :
    0 < x < pi/2 and 0 < x +T < pi/2
    sin(x+T) + cos(x+T) = sinx + cosx
    Multiplying and dividing by sqrt2
    sin(x + T + pi/4) = sin(x + pi/4)
    T = 0 , 2pi , 4pi
    No solution

    Case 2 :
    0<x<pi/2 and pi/2 < x+T <pi
    sin(x+T) - cos(x+T) = sinx + cosx [ Look at the -ve sign]
    Multiplying and dividing by sqrt2
    sin(x + T - pi/4) = sin(x + pi/4)
    T = pi/2
    Thus , pi/2 is the solution.
    Try drawing the graph and you will understand more clearly !!

    Hope this helps .... Keep posting !!
  • hey Friction! Thats a nice approach...good one! keep it up!

    by the way howz IIT goin?

    You back after a long time on KB!
  • Hi Ankita ..... thanks ...

    life's good in iit .... yeah I am bak after a while

    I was a little busy .. Neways how are ?
  • Yea i year i really very very busy with placements and projects, when I was in Kanpur, I was half dead during my projet!!

    My prof really made to work for the paper!!

    anywayz....past is past... :-)

    Life's good now!!
  • Hey by the way Shashank....did u like!

    and Yes, throw more questions at us!! Its fun!

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