## haleyelizabeth2017 one year ago 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 ______

1. anonymous

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

2. haleyelizabeth2017

Wait...20 is midline actually I think

3. anonymous

20 is amplitude

4. haleyelizabeth2017

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

5. anonymous

ok yeah

6. haleyelizabeth2017

:) how do I figure out the second part?

7. anonymous

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

8. haleyelizabeth2017

Which is 6.25 hours...so 13.5?

9. haleyelizabeth2017

And then I divide 2pi by that?

10. anonymous

12.5 hrs. and then yes divide 2π by that

11. 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

12. haleyelizabeth2017

Wait! forgot x

13. haleyelizabeth2017

...or theta.

14. anonymous

yes. and I think there's a shift

15. haleyelizabeth2017

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

16. haleyelizabeth2017

Like it depends which way I thought...

17. haleyelizabeth2017

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

18. anonymous

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

19. anonymous

$32-20\cos \frac{ \pi x}{ 6.25 }$

20. haleyelizabeth2017

21. anonymous

yest

22. haleyelizabeth2017

Ah...is that all?

23. anonymous

yes

24. haleyelizabeth2017

Awesome! Thank you!

25. anonymous

you're welcome