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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