# Periodic functions

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• Dec 2nd 2010, 07:04 PM
terminator
Periodic functions
see attached
• Dec 2nd 2010, 08:23 PM
BAdhi
a)check out my definitions, please mention if they are wrong..
amplitude is the distant between a max and min (i.e. 4.5-1 =3.5)
length of a periodic cycle = period (i.e.3.5pi - (-.5pi))
horizontal shift = horizontal shift from the normal sin wave (i.e. amplitude/2-1)
vertical shift= when y=horizontal shift , the least value of x
• Dec 3rd 2010, 01:15 PM
terminator
just about
Attachment 19946This is what I got.
see attached
• Dec 4th 2010, 06:46 AM
BAdhi
sorry :( i was wrong

since the main idea of finding the values of the variables is getting equation of the graph, one can deduce from the equation of the normal sine wave.

for example,

f(x) = sin(x) (amplitude = 1)

to make the amplitude = a

f1(x) = a.sin(x)

then shift the wave up d number of units,

f2(x) = a.sin(x) + d

then move the wave left c number of units,

f3(x) = a.sin(x+c) +d

will it be correct this way?

but what do you mean by period =$\displaystyle \frac{2\pi}{b}$
• Dec 4th 2010, 07:40 AM
e^(i*pi)
Quote:

Originally Posted by BAdhi
but what do you mean by period =$\displaystyle \frac{2\pi}{b}$

I suspect (and only guess because I don't download and open files from the internet!) that it's related to $\displaystyle f(x) = A\sin(Bx+C) + D$ where A, C and D are as defined in the post above.

The period, is the "time/distance" it takes to reach the same point. For a standard sin or cos graph the period is $\displaystyle 2\pi$. As B is the amount the graph is compressed by this is going to change the period.

It is divided by B (rather than multiplied) because the graph reaches the same point more quickly for large values of B.