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Thread: finding the period of an equation

  1. #1
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    finding the period of an equation

    How would you find the period of y=-4sin(pi/3)x ?

    -sorry, i dont know how to put the pi sybol in so I wrotwe it

    -thanks for any help, J.T.
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  2. #2
    o_O
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    Given the general periodic function: $\displaystyle y = A\sin(B(x + C)) + D$

    The period is given by: $\displaystyle \frac{2\pi}{B}$
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  3. #3
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    Hi !
    Quote Originally Posted by jem7vwhjt View Post
    How would you find the period of y=-4sin(pi/3)x ?

    -sorry, i dont know how to put the pi sybol in so I wrotwe it

    -thanks for any help, J.T.
    Welcome in the forum ! There's the latex in here, just do $\displaystyle \pi$ or $\displaystyle y=-4 \sin \left(\frac{\pi}{3} x \right)$
    See here : http://www.mathhelpforum.com/math-help/latex-help/ for more codes.

    For your problem. The period T is defined such that f(x+T)=f(x).

    So here $\displaystyle f(x+T)=-4 \sin \left(\frac{\pi}{3} (x+T) \right)$

    You know that the sine function is $\displaystyle \underline{2 \pi}$ periodic. So it would be nice to find T such that we get this $\displaystyle 2 \pi$

    Develop f(x+T) :
    $\displaystyle \begin{aligned} f(x+T) &=-4 \sin \left(\frac{\pi}{3} (x+T) \right) \\
    &=\underbrace{-4 \sin (\tfrac{\pi}{3} x}_{\text{this is f(x)}}+\tfrac{\pi}{3} T ) \end{aligned}$

    So find T such that $\displaystyle \frac{\pi}{3} T=2 \pi$ and you're done
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    thank you
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