Math Help - Applications of periodic functions : tides and times

1. Applications of periodic functions : tides and times

On a typical day at a seaport, the water has a maximum depth of 16 m at 7:00 AM. The minimum depth of 4m occurs at 1:24 PM. Assume that the relation between depth h, in metres, and the time t, in hours, is a sinusoidal function.

a) write an equation for h for any time, t hours.

My answer: $h= 6 {\cos}\frac{\pi}{6.4}(t-7)+10$ (in radians)

b) Give the depth h at 10:30 QM (accurate to two decimals)

My Answer: 10:30 = 10.5 hours, I punched my equation into my TI-83 Plus and I got 9.12 as the value

c) find two times before noon when h is 14m (accurately to the nearest minute)

Here's my problem; I punched in a second equation $y_{2}= 14$ and then found the intersects, but I that gives me decimals which are not as simple to convert from hundredths of hours to minutes. How can I make the conversion easily? and am I going about this question correctly?

2. Originally Posted by Coren
...

c) find two times before noon when h is 14m (accurately to the nearest minute)

Here's my problem; I punched in a second equation $y_{2}= 14$ and then found the intersects, but I that gives me decimals which are not as simple to convert from hundredths of hours to minutes. How can I make the conversion easily? and am I going about this question correctly?
1. The times when the the water has a depth of 14 m are

$t_1 = 5.28659\ o'clock$ an

$t_2 = 8.71341\ o'clock$

2. Since you are allowed to use a TI83 and since the number format of hours-minutes-seconds is similar to the number format of degrees-minutes-seconds you can use the build-in function DMS:

- type the result and press enter
- then use 2ND ANGLE 4 = DMS and type enter
- interpret the result as 5 o'clock and 17 minutes and 11.2 seconds
- see attachment