Thread: Circular Functions Application

1. Circular Functions Application

Question Is:

It is suggested that the height h(t) meters of the tide above mean sea level on 1st january at Warnung is given approximately by the rule h(t) = 4sin(pi/6t), where t is the number of hours after midnight.

A) when was high tide?
B) what was the height of the tide?
C) what was the height of the tide at 8 am?
D) a boat can only cross the harbour bar when the tide is atleast 1 meter above mean sea level. when could the boat cross the harbour bar on 1st january?

please i need help with this

2. If I understand the question (as I'm not so good in English):
answers
A) the sinus function is maximum at pi/2, 2pi+pi/2, 4pi+pi/2, ..., 2n*pi + pi/2...
pi/6 * t = pi/2 , you get t = 3
pi/6 * t = 2pi +pi/2 = 5pi/2 , you get t = 15
pi/6 * t = 4pi +pi/2 = 9pi/2 , you get t = 27 (which is greater then the number of the hours in one day)
So high tide was at 3 and 15 (3pm).
B) the maximum value of the sinus function is 1, so 4*1 = 4
C) just put t = 8: 4sin(pi/6 * 8) = 4sin(pi * 4/3) = 4 * (-0.5) = -2
D) You must find when h is 1. 1 = 4sin(pi/6t), with the calculator (put the DRG to radians!!!) you can find sin-1 of 1/4 is 0.25268... so t = 0.48...
If you sketch the tide you can see that it goes down under 1 again at 6-0.48=5.52 (because of symmetry). And the situation repeats after 12 hours. So the boat can cross from 0.48 to 5.52 and from 12.58 to 17.52.