Question

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?

Answer 1

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.