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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- Aug 26th 2008, 01:40 PMjem7vwhjtfinding 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. - Aug 26th 2008, 02:06 PMo_O
Given the general periodic function: $\displaystyle y = A\sin(B(x + C)) + D$

The period is given by: $\displaystyle \frac{2\pi}{B}$ - Aug 26th 2008, 02:09 PMMoo
Hi !

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 (Wink) - Aug 26th 2008, 04:22 PMjem7vwhjt
thank you