1. ## Depth-Time

The pool surrounding... blahblahb... the depth (in meters) was modeled by the function h with the rule h(t) = 10 + 5cos((pi/36)t) where t is the time in hours after 1.00 am on January 1. State the minimum and maximum depths and the times that they occur in one day.

From the function, I know that the minimum depth is 5 and the maximum is 15. I also know that the period of the function is 72 hours (i.e. 3 days). Therefore, 36 hours after 1.00 am the height of the water is at its lowest point. It's at its highest point 0 and 72 hours after 1.00 am. These times translate to 15 m at 1 am on Jan 1 and Jan 3, and 5 m at 1 pm on Jan 2. That all seems pretty straight forward (assuming I did it correctly). What confuses me about the question, however, is when it asks to state the times that the minimum and maximum depths occur in one day. One day would only be 1/3 of a cycle, which only includes 1 occurrence of either depths (maximum at 1 am on Jan 1). Or, as I just realised while writing this, is it asking to state the times that they occur each day, in which case I'm correct?

Sorry if the wording is a little bit choppy, I'm in a bit of a rush.

Thank you for your help, it is greatly appreciated.

2. ## Re: Depth-Time

Hi Fratricide,

I think that you are correct except for a little careless error, the second 15m depth occurs at 1am on 4th January.

I think the actually question is worded very poorly. I'd just cover my bases by telling the whole story. State the max and min times and depths for the entire 3 days - and then give the maximum and minimum times and depths for each of those days individually.