Results 1 to 2 of 2

Math Help - Trig application problems.

  1. #1
    Junior Member
    Joined
    May 2010
    Posts
    36

    Trig application problems.

    Hi,
    I`m having a lot of trouble solving the following question:


    The water at a local beach has an average depth of 1 metre at low tide. The average depth of the water at high tide is 8 m. If one cycle takes 12 hours:
      1. Determine the equation of this periodic function using cosine as the base function where 0 time is the beginning of high tide.
      2. What is the depth of the water at 2 am?
      3. Many people dive into the beach from the nearby dock. If the water must be at least 3 m deep to dive safely, between what daylight hours should people dive?

    I am really confused about this problem, and dont even know how to start

    Any helpful tips will be greatly appreciated.

    Thanks!
    Last edited by mr fantastic; June 5th 2010 at 04:46 PM. Reason: Edited post title.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Mar 2010
    Posts
    993
    Thanks
    244
    1. The height is given by h(t)=h_{avg}+A\cos{\omega{t}}. Normally there would be a phase variable, but we are given that there is a maximum at t=0, so the phase must be zero. The difference between high and low tide is (h_{avg}+A)-(h_{avg}-A)=2A=8-1=7, so A=3.5 and since the max is 8, h_{avg}=8-3.5=4.5 (I could have also used the min). Since one cycle is 12 hours, \omega=\frac{2\pi}{12}=\frac{\pi}{6}. So the equation is:

    h(t)=4.5+3.5\cos{\frac{\pi}{6}t}

    The other two problems just work with this equation. For (2), you set t=2 and find h(t). For (3), you need to know what range of t makes h(t) is greater than or equal to 3.

    Post again in this thread if you're still having problems.

    - Hollywood
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. application problems
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: February 9th 2010, 01:30 AM
  2. Application Problems
    Posted in the Algebra Forum
    Replies: 6
    Last Post: November 29th 2008, 12:30 PM
  3. Assistance with application problems
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 3rd 2007, 01:51 PM
  4. application problems
    Posted in the Calculus Forum
    Replies: 7
    Last Post: June 3rd 2007, 04:22 PM
  5. A few antiderivative application problems
    Posted in the Calculus Forum
    Replies: 3
    Last Post: January 23rd 2007, 11:29 PM

Search Tags


/mathhelpforum @mathhelpforum