Question

help!!

Answer 1

how do I write the equation of the graph?

Answer 2

Tell me what the graph of y = cos x looks like.

Answer 3

its (0,1) (pi,-1) (2pi,1) (3pi,-1) etc

Answer 4

but with the dots in um the up and down motions (from half of 0 and pi , pi and 2pi,

Answer 5

So what is the difference between this one and cosx?

Answer 6

its sin ? and the graph is given but I don't know how to get an equation

Answer 7

nvm its cos

Answer 8

The sine function is zero when x = 0.
A cosine function is 1 when x = 0.

So we need to choose the acos(bx) here.

a is the amplitude. Amplitude is how much above or how much below the mean line (which is x axis here) the curve swings. Could you figure out the amplitude from the diagram?

Answer 9

a = 3

Answer 10

so y = 3cos.. bx

Answer 11

Yes. a = 3.

So the equation is y = 3cos(bx). We still need to figure out b.

The period of a cosine or a sine function is how long before the curve repeats itself. Could you look at two successive peaks in the diagram and figure out after how much x the function repeats itself?

Answer 12

every 3pi?

Answer 13

or every 6pi/2?

Answer 14

No. The curve attains a peak at x = 0. The next peak occurs at x = 6pi.
The period is how much x has passed before the curve starts to repeat itself.
So what is the x distance between peak-to-peak?

Answer 15

6pi/2

Answer 16

No. At x = 0, first peak. At x = 6pi the next peak.
The difference in x is: 6pi - 0 = 6pi.

Every 6pi the curve repeats itself. You can take the distance between two successive low points also and it will still be 6pi.

So the period of this curve is 6pi.

Answer 17

OH

Answer 18

y=3cos (6pi)x ?

Answer 19

The formula for the period of cos(bx) is: Period = 2pi / b

Looking at the graph we found the period to be 6pi. Plug that into the formula:
6pi = 2pi / b
Find b.

Answer 20

2pi/6pi = pi/3pi

Answer 21

The pi will cancel out. so b = ?

Answer 22

yes sorry

Answer 23

1/3

Answer 24

Yes. Put them all together and the curve represented in the graph is: y = 3cos(1/3*x)

Answer 25

okay thank you!! a lot!

Answer 26

You are welcome.