Question

PLEASE HELP! E,F,G only!

Answer 1

this is doable but it is going to take a few minutes
did you get the range?

Answer 2

16.5<Y<32.6

Answer 3

oh sorry forgot about you
ok that is a range of \(16.1\)

Answer 4

i mean of length 16.1, half of that is \(8.05\) so that is your amplitude

Answer 5

or as it says in you question \(a=8.05\)

Answer 6

january is the low point right?

Answer 7

and june is the high
so we want \(0\) which is january to correspond to ...
before we continue, you using degrees or radians? can't continue without that

Answer 8

Degrees

Answer 9

ok so we want 0 to go to the minimum value of sine, which is when \(x=-90\) or if you prefer \(270\)
lets stick with \(-90\)

Answer 10

the period is \(12\) months, so we put \(\frac{360}{b}=12\) and solve for \(b\)

Answer 11

that makes \(b=30\)

Answer 12

b=30

Answer 13

right

Answer 14

you want to plug in 0 and get -90, plug in 12 and get 270 we can solve
\(30x-90\) as your input

Answer 15

really we didn't need all that
knew that \(b=30\) and zero should give you -90

Answer 16

so now we are at
\[y=8.05\sin(30x-90)\] but now quite done

Answer 17

oops not quite done i mean

Answer 18

if you put \(x=0\) you get
\[8.05\sin(-90)=-8.05\] but you don't want \(-8.05\) you want \(16.5\) so you have to raise it up

Answer 19

that is the number you need out at the end \(16.5+8.05=24.55\)

Answer 20

\[y=8.05\sin(30x-90)+24.55\] should make all this work

Answer 21

so thats the answer to g?

Answer 22

i think so
lets check

Answer 23

http://www.wolframalpha.com/input/?i=y%3D8.05sin%2830x^o-90%29%2B24.55+domain+0..12
looks good

Answer 24

thank you so much!

Answer 25

do you understand what question f is referring too? For me G and F are kind of the same thing

Answer 26

sorry I mean E and F

Answer 27

no not really

Answer 28

guess you are supposed to say "a is the amplitude" or whatever
whatever it says in the book

Answer 29

okay so is e asking for the general idea of what a b c and d are?

Answer 30

example: a=amplitude, b=period, c=phase shift and d=vertical shift

Answer 31

yes i think so

Answer 32

except \(b\) is not the period
it determines the perios
the perios is \(\frac{360}{b}\)

Answer 33

*period

Answer 34

btw i see that they write this as
\[a\sin[b(t-c)]+d\] so you could also write
\[y=8.05\sin[30(t-30)]+24.55\] same thing we had above

Answer 35

okay

Answer 36

so then in terms of the time function what would all those values equal? dont they still equal the same thing? Im confused

Answer 37

it is identical to the one i wrote above
same thing exactly, i just factored out the \(30\) because that is how it was written on your question

Answer 38

oh yes I know haha I mean the values a,b,c and d for question F

Answer 39

don't fret about that it makes no difference at all
not sure why they wrote it the way they did

Answer 40

\(a\) is the amplitude, it is half the length of the range

Answer 41

\(b\) determines the period, the period is \(\frac{360}{b}\) which in your case is \(12\) making \(b=30\)

Answer 42

\(c\) is the phase shift

Answer 43

well actually \(bc\) is the phase shift, we shifted 90 degrees to the left

Answer 44

and \(d\) raises or lowers the function
in this case we had to raise it up to make it go from min to max correctly

Answer 45

whew now i am exhausted

Answer 46

haha okay I understand thanks @satellite73

Answer 47

yw
you gotta turn this in or something?

Answer 48

nawh not really just studying for an exam and this was a previous question I got stuck on and thought I should resolve before the test

Answer 49

good luck!

Answer 50

thanks!