Question

The water level varies from 12 inches at low tide to 52 inches at high tide. Low tide occurs at 9:15 a.m. and high tide occurs at 3:30 p.m. What is a cosine function that models the variation in inches above and below the water level as a function of time in hours since 9:15 a.m.

I have the first part of it, I just need helping finding the last bit of the function. So far I have 44 + 32 cos ______

Answer 1

I don't think the 44 and 32 are right.

Answer 2

Wait...20 is midline actually I think

Answer 3

20 is amplitude

Answer 4

Whoops...wasn't thinking lol 32 + 20 cos :P

Answer 5

ok yeah

Answer 6

:) how do I figure out the second part?

Answer 7

the period is going to be twice the time between 9:15 am and 3:30 pm

Answer 8

Which is 6.25 hours...so 13.5?

Answer 9

And then I divide 2pi by that?

Answer 10

12.5 hrs. and then yes divide 2π by that

Answer 11

Ah! Sorry...brain's not wanting to work today :( did that earlier too haha

so I got:
\[32 + 20 cos \frac{\pi}{6.25}\]
we didn't really even need to multiply it by 2 :P

Answer 12

Wait! forgot x

Answer 13

...or theta.

Answer 14

yes. and I think there's a shift

Answer 15

Ah. wouldn't that be x +/- something?

Answer 16

Like it depends which way I thought...

Answer 17

so \[32 + 20 cos \frac{\pi}{6.25}(x+9.25) \]
maybe?

Answer 18

yes. but since you shifted by half you could just switch the sign

Answer 19

\[32-20\cos \frac{ \pi x}{ 6.25 }\]

Answer 20

instead of adding 9.25? O.o

Answer 21

yest

Answer 22

Ah...is that all?

Answer 23

yes

Answer 24

Awesome! Thank you!

Answer 25

you're welcome