see attached
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
definitions-periodic functions.docThis is what I got.
see attached
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 =$\displaystyle \frac{2\pi}{b}$
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.