Question

6) The height h(t) meters above the tide above sea level on January 24th at Cape Town is modeled approximately by h(t)=3sin(30t) where, ‘t’ is the number of hours after midnight. II. When is the high tide ?

Please give an answer with working out. Thanks :)

Answer 1

The height h(t) meters of the tide above sea level on January 24th at Cape Town is modeled approximately by h(t)=3sin(30t) where, ‘t’ is the number of hours after midnight. When is the high tide ?*

Answer 2

\[h(t) \approx 3\sin(30t)\]The high tide will occur when \[\sin(30t) = 1\] which is the maximum value of the \(\sin\) function. What is the first value of \(\theta\) going around the unit circle where \(\sin \theta = 1\)? Set \(30t = \theta\) and solve for t.

Note well that the function assumes you are computing sin of a value in degrees, not radians.

Answer 3

Thank you ! how did you tell whether it functions for values in radians or degrees?

Answer 4

Do you have an answer yet to when the high tide is?

Answer 5

yeah what i got was t=0.2093n + 0.052 where n>-1
that is in hours

Answer 6

If you're working in radians, \(\sin \theta =1 \) at \(\theta = \pi/2 \approx 1.57\). That means the high tide is only a minute or so past midnight (not impossible, but read on) and that in the course of 1 hour, the tide goes in and out \(30/(2\pi) \approx 4.8\) times! Now, if you're working in degrees, going once around the unit circle is 360 degrees, and 30t = 360 means that a full tide cycle takes 12 hours, which is about right.

No, I think you didn't do it right...

Answer 7

Here's a graph of the tide equation in radians (purple) and degrees (blue). Note that the graph only covers half an hour!

Answer 8

Here's the tide function, working in degrees, and covering an entire day.