Thread: 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. 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!

1. The height is given by . 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 , so and since the max is 8, (I could have also used the min). Since one cycle is 12 hours, . So the equation is:



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