haleyelizabeth2017
  • haleyelizabeth2017
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 ______
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
I don't think the 44 and 32 are right.
haleyelizabeth2017
  • haleyelizabeth2017
Wait...20 is midline actually I think
anonymous
  • anonymous
20 is amplitude

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haleyelizabeth2017
  • haleyelizabeth2017
Whoops...wasn't thinking lol 32 + 20 cos :P
anonymous
  • anonymous
ok yeah
haleyelizabeth2017
  • haleyelizabeth2017
:) how do I figure out the second part?
anonymous
  • anonymous
the period is going to be twice the time between 9:15 am and 3:30 pm
haleyelizabeth2017
  • haleyelizabeth2017
Which is 6.25 hours...so 13.5?
haleyelizabeth2017
  • haleyelizabeth2017
And then I divide 2pi by that?
anonymous
  • anonymous
12.5 hrs. and then yes divide 2π by that
haleyelizabeth2017
  • haleyelizabeth2017
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
haleyelizabeth2017
  • haleyelizabeth2017
Wait! forgot x
haleyelizabeth2017
  • haleyelizabeth2017
...or theta.
anonymous
  • anonymous
yes. and I think there's a shift
haleyelizabeth2017
  • haleyelizabeth2017
Ah. wouldn't that be x +/- something?
haleyelizabeth2017
  • haleyelizabeth2017
Like it depends which way I thought...
haleyelizabeth2017
  • haleyelizabeth2017
so \[32 + 20 cos \frac{\pi}{6.25}(x+9.25) \] maybe?
anonymous
  • anonymous
yes. but since you shifted by half you could just switch the sign
anonymous
  • anonymous
\[32-20\cos \frac{ \pi x}{ 6.25 }\]
haleyelizabeth2017
  • haleyelizabeth2017
instead of adding 9.25? O.o
anonymous
  • anonymous
yest
haleyelizabeth2017
  • haleyelizabeth2017
Ah...is that all?
anonymous
  • anonymous
yes
haleyelizabeth2017
  • haleyelizabeth2017
Awesome! Thank you!
anonymous
  • anonymous
you're welcome

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