Please could you explain it steps by steps?
A small natural harbour in Cornwall is protected from bad weather by a natural rock barrier. Unfortunately, this means that the harbour is not accessible during certain times of the day. On a particular day the depth of water, d metres, beyond the barrier is modelled by the function:
d(t)=4sin(pi t/8) + 12
Where t is the time in hours after 06:00 (when t = 0)
(a) What is the depth of water at 08:00.
Given the function :
d(t) = 4sin( pi*t/8) + 12
Where d is the depth in metres and t is the time in hours.
At the initial time ( 6:00 or t=0) the depth is 12 meters.
We need to find the depth at the following tines:
That means that the time is 2 hours after the initial times.
==> t= 2.
==> d(2) = 4sin(2*pi/8) + 12 = 4*sin(pi/4) + 12
We know that sin(pi/4) = sqrt2/2
==> d(2) = 4*sqrt2/2 + 12 = 2sqrt2 + 12 = 14.828 m
Then, the depth at 8:00 is 14.828 m.