Question

finding equations for trig graphs?

Answer 1

it's these four and all I know how to do is find the amplitude which is the easiest part. Could someone help me out?

Answer 2

what else do you need ?

Answer 3

Finding the function associated with the graph

Answer 4

ok wanna do the first one?

Answer 5

If you're up for it yeah

Answer 6

what did you get for the amplitude?

Answer 7

+2

Answer 8

if that's wrong i s2g.

Answer 9

it is 2, right

Answer 10

it goes from \(-5\) to \(-1\) which has length 4 so the amplitude is 2
to make it go from \(-2\) to \(2\) you are going to have to lift it up 3 units

Answer 11

did you get the period?

Answer 12

I think it's either 6 or 12

Answer 13

oh no

Answer 14

look at the top most point of the graph, where the curve is at \(-1\)
one is where \(x=\frac{\pi}{4}\)
where is the next one?

Answer 15

5x/4

Answer 16

right
well \(\frac{5\pi}{4}\)

Answer 17

new to openstudy my bad

Answer 18

no problem
in any case the period it the length of that interval, the length of
\[[\frac{\pi}{4},\frac{5\pi}{4}]\]
aka \(\frac{5\pi}{4}-\frac{\pi}{4}\)

Answer 19

on other words the period is \(\pi\)

Answer 20

okay good, I actually understand that

Answer 21

you know \(\sin(bx)\) has period \(\frac{2\pi}{b}\) set
\[\frac{2\pi}{b}=\pi\] and solve for \(b\)

Answer 22

let me know when you get \(b=2\)

Answer 23

so,
\[b = 2\]

Answer 24

oh, yeah I got that

Answer 25

right
now we have the amplitude is 2, \(b=2\) and it looks like sine shifted down 3 units

Answer 26

final answer
\[y=2\sin(2x)-3\] btw i guess we should say why it is sine and not cosine

Answer 27

if you shift this one up 3 units it goes right through \((0,0)\) and \(\sin(0)=0\) so it is sine shifted down

Answer 28

as compared to the next one, the one below it, that looks like cosine shifted down

Answer 29

so, if I understand this, sine cannot go through \[(0,0)\] but cosine can

Answer 30

if I'm wrong I apologize I'm a little slow with this

Answer 31

sine goes through \((0,0)\)

Answer 32

that is how i know this is sine
it is sine shifted down

Answer 33

but it's shifted down 3 okay I get it

Answer 34

here is a graph of both \(y=2\sin(x)-3\) and \(y=\sin(x)\)
http://www.wolframalpha.com/input/?i=2sin%282x%29-3%2Csin%28x%29

Answer 35

the next one is cosine, because cosine has its maximum at 0, as does this graph
the amplitude is easy to find, the period is easy too if you understand how to see it

Answer 36

gotta run to class, good luck!

Answer 37

okay thank you so much I really appreciate the help!