The height, h, in metres of the tide in a given location on a given day at t hours after midnight can be modelled using the sinusoidal function h(t) = 5sin(30(t-5))+7 What time is the high tide?What time is the low tide?

Is this question related to either the maximum or the minimum value of the graph. Does the period play a role here as well?

1 Answer
Sep 22, 2016

The height, h, in metres of the tide in a given location on a given day at t hours after midnight can be modelled using the sinusoidal function
h(t) = 5sin(30(t-5))+7

"At the time of high tide "h(t) "will be maximum when " sin(30(t-5))" is maximum"

"This means " sin(30(t-5))=1
=>30(t-5)=90=>t=8
So first high tide after midnight will be at 8" am"

Again for next high tide 30(t-5)=450=>t=20
This means second high tide will be at 8" pm"

So at 12 hr interval the high tide will come.

"At the time of low tide "h(t) "will be minimum when " sin(30(t-5))" is minimum"

"This means " sin(30(t-5))=-1
=>30(t-5)=-90=>t=2
So first low tide after midnight will be at 2" am"

Again for next low tide 30(t-5)=270=>t=14
This means second low tide will be at 2" pm"

So after 12 hr interval the low tide will come.

Here period is(2pi)/omega =360/30hr=12hr so this will be interval between two consecutive high tide or between two consecutive low tide.