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so we have a sinusoidal graph we don't
know right now if it's sine or cosine
but all sinusoidal graphs have a midline
and amplitude in a period now the
midline is the line in the middle of it
but it's a horizontal line in the middle
of it
so if you kind of look at this carefully
I hope you can see there's a horizontal
line right there through the middle of
it that horizontal line is the equation
y equals negative 1 and that is your
middle line your midline so our midline
is y equals negative 1
next your amplitude now amplitude if you
think about amplitude amplitude well
ever think about music amplitude is kind
of like it amps up the music makes it
bigger makes it a bigger wave bigger
sound or if you take a if you guys take
a red bowl or something you're amping
yourself up you're increasing your
energy so can you see it from the
midline can you see how how high it is
is called your amplitude you're
increasing its vertical stretch so our
amplitude here is how high you went or
how low you went is it the same for the
midline it's the same up and down
see how it's the same and what you'll
see here is what did we go up we went up
to and we went down to so what you can
see here is your amplitude is 2 because
from the midline you're going up two
down two up two down to in a very
cyclical periodic manner now the last
piece is called your period now a period
is just like school you have periods
don't you start a period into period
repeat in class don't you do something
and then redo it another cross same
thing repeat repeat and jaqi they have
periods because you do a certain thing
and you repeat it again three times
during the game so that's what these are
we want the period the repeating cycle
so what we got here is well hmm if I
want a repeating cycle well watch this
if I started here don't we repeat right
there
can you see if I kind of went across
right there if I went across from there
boom boom boom boom boom
wouldn't that be one cycle from there
don't you repeat over and over again so
what is the width of that cycle it is
two so every two units of X you are
going to repeat the graph the period
repeats so the period is your horizontal
stretch how much the stretch side to
side of how much it's how long before it
repeats itself just like I just repeated
myself so for this particular graph I
want to find the midline amplitude
period so the midline again is the line
through the middle of it little bit
harder to see here so I'm gonna do a
little computation can you tell the
highest here is five and the lowest is
negative one so if you want the middle
of five and negative one watch this
could you take five plus negative one
and average it is an average mean middle
when you do that don't you get 4 divided
by 2 which is 2 so guess what your
midline is 2 and watch what happens at 2
do you see the middle of your graph kind
of nice if you average the high and lows
you'll get the middle and that's your
midline next I want to find the
amplitude well amplitude is how high or
low it goes from the midline so find any
spot from the midline go up and down
count how far that is and you will see
for this particular problem you're going
up 3 and you're going down 3 so your
amplitude is 3 and lastly your period or
your period well let's just say we start
here some people want to say your period
stops here but no doesn't it go down and
back that's where your period ends ok
one cycle would look like that or start
here one cycle looks like that it's
wherever you start and you end and the
whole graph has been made
and then it repeats so this right here
is your period and for this one it is
that value because you're going from 0
to 2 PI over 3 so the period for this
one is 2 pi divided by 3 because from
here to here 0 2 that would be the
length of one cycle
