Came across this question the other day in a class revision exercise:
The height of tides is given by the equation where t is hours after midnight and h is metres.
I was able to draw the graph, find the amplitude and period quite easily but could not solve for periods over >1 in terms of height so that a boat would be able to cross the sandbar safely.

So my question is how is it possible to solve the times at which h(t)>1?

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1 Answer

Was this a non-calculator question?

If you can draw the graph, all you need to do now is to figure out when h(t) = 1.
Then, from the graph you will be able to see the domain (t values) where h(t) > 1

To figure out this, you may need a calculator, as the equation you have to solve becomes:

h(t) = 1
4sin(./6t) = 1
sin(./6t) = 1/4

The basic angle for 1/4 is not a known exact value. You'd proceed by using sin-1(1/4) to get an inexact value for it.

Let me know if this helps - if not, please try to clarify and I'll do my best to fix my answer.

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