Question

The curve above is the graph of a sinusoidal function. It goes through the point (7,2). Find a sinusoidal function that matches the given graph

Answer 1

@hartnn

Answer 2

A sinusoidal curve is going to be in the following form: \[
f(t) = a\sin(\omega t+\phi)
\]

Answer 3

Where \(a\) is the amplitude, \(\omega\) is the frequency, and \(\phi\) is the phase shift.

Answer 4

i am aware of the prior information.

Answer 5

First let's find \(a\).
To find the amplitude, you want to find the difference between the top and bottom and divide by 2.

Answer 6

thus far i have 2cos5.25

Answer 7

\(2\cos(5.25)\)?

Answer 8

That isn't a function...

Answer 9

dont make me feel stupid or i will most certainly block you...

Answer 10

i realize that is not a function.

Answer 11

Why don't you explain then?

Answer 12

i was informing you on what i had so far. if that isn't right then you can tell me what i am doing wrong... i am here for help.

Answer 13

i got 5.25 because 21/4 = 5.25

Answer 14

which i assumed to be "T"

Answer 15

T as in the period?

Answer 16

the 2 comes from the graph's min-max

Answer 17

yes.

Answer 18

"T" as in the period.

Answer 19

Well, 21 gets you you a period and a half.

Answer 20

21 is one and a half wave lengths. The period is just one wave length.

Answer 21

okay. i understand that now. i see where i was doing that wrong.

Answer 22

i just need B

Answer 23

and how to find "B" by looking at the graph

Answer 24

B?

Answer 25

Is that the phase shift or something?

Answer 26

Can you tell me what your equation is?

Answer 27

Asin(Bx+C)

Answer 28

there will be no phase shift and period is 2pi/B

Answer 29

sin is interchangeable with trig functions.

Answer 30

idk the equation. that is what i am trying to figure out by just looking at the graph.

Answer 31

The period is 14, that is the distance from two tops.

Answer 32

That makes \(B=2\pi/14\), no?

Answer 33

Because at \(0\), \(Bx=0\) and at \(14\) , \(Bx=2\pi\)

Answer 34

so the equation is still not clear to me... idk how you got 14.