# 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?

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
$h \left(t\right) = 5 \sin \left(30 \left(t - 5\right)\right) + 7$

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

$\text{This means } \sin \left(30 \left(t - 5\right)\right) = 1$
$\implies 30 \left(t - 5\right) = 90 \implies t = 8$
So first high tide after midnight will be at $8 \text{ am}$

Again for next high tide $30 \left(t - 5\right) = 450 \implies t = 20$
This means second high tide will be at $8 \text{ pm}$

So at 12 hr interval the high tide will come.

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

$\text{This means } \sin \left(30 \left(t - 5\right)\right) = - 1$
$\implies 30 \left(t - 5\right) = - 90 \implies t = 2$
So first low tide after midnight will be at $2 \text{ am}$

Again for next low tide $30 \left(t - 5\right) = 270 \implies t = 14$
This means second low tide will be at $2 \text{ pm}$

So after 12 hr interval the low tide will come.

Here period is$\frac{2 \pi}{\omega} = \frac{360}{30} h r = 12 h r$ so this will be interval between two consecutive high tide or between two consecutive low tide.