# 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...

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.

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

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:

a) 8:00

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.