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
P dilip_k
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.

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