The height of the tide in a given location on a given day is modelled using the sinusoidal function h(t)=5 sin (30(t-5))+7. a) What time is high tide? What time is low tide?

Answer 1

So you want the t value which produces the max and min of the function, that is,
h '(t) = 0
5cos30(t-5) (30) = 0
cos 30(t-5) = 0
we know cos π/2 = 0 and cos 3π/2 = 0
30(t-5) = π/2 or 30(t-5) = 3π/2
t = 5.052 or t = 5.157

You did not define t, so you will have to make sense out of the value of t above.