Fundamental period?

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mattflint50

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Apr 25, 2005
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My clalculus class is reviewing for the AB exam. We were assigned to do a practice test and on it there is a question that asks me to find the fundamental period of an equation. What does this meen, and how can it be done?

Thanks for your help
 
They may be talking about trig functions in the sense that they repeat their values.

Sine and cosine repeat every \(\displaystyle 2{\pi}\) units and the tangent function

repeats every \(\displaystyle {\pi}\) units.
 
so if the equation was y=2-3sin Pi/4 (x-1) how would i determine the fundamental period
 
The function

\(\displaystyle \mbox{ y = A\sin{\left(B(x + C)\right)} + D}\)

has (fundamental) period \(\displaystyle \L\mbox{\frac{2\pi}{B},}\) assuming radian measure.
 
The answers I have to choose from are 1/8, pi/4, 4/pi 8 ,and 2pi. Would it be 2pi in this case?
 
ummmm? I am confused as to how you broke up that equation. But my guess would be pi/4 or 1.
 
I am also confused. Can you explain how you broke that equation up. If I had to guess I would say pi/4 or 1 as well.
 
It is just something you need to learn.

Your equation

\(\displaystyle \mbox{ y = 2 - 3\sin{\left(\frac{\pi}{4}(x - 1)\right)}}\)

ie.

\(\displaystyle \mbox{ y = -3\sin{\left(\frac{\pi}{4}(x - 1)\right)} + 2}\)

Compares with the general equation

\(\displaystyle \mbox{ y = A\sin{\left(B(x + C)\right)} + D}\)

\(\displaystyle \mbox{ }\)which has amplitude \(\displaystyle A\) (well, the absolute value of), period \(\displaystyle \mbox{\frac{2\pi}{B}}\), and is translated horizontally and vertically by \(\displaystyle \mbox{-C}\) and \(\displaystyle \mbox{D}\), respectively.
 
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