GCSE Maths Question

The following question was found on an Edexcel paper.

I have work out an answer using trial and error. Could someone tell me the real way?

The depth, D meters, of the water at the end of a jetty in the afternoon can be modelled by this formula:

D= 5.5 + Asin30(t-k)°

Where:

t hours is the number of hours after midday.
A and K are constants.

Yesterday the low tide was at three pm.
The depth of water at low tide was 3.5m.

Find the value of A and K.

Any solutions would be appreciated.

Please explain your working.

Reply 1

Jonny W

As t varies, 5.5 + Asin[30(t - k)] varies from 5.5 - A to 5.5 + A (because sin(t) goes from -1 to 1.)

Since low tide is 3.5m it follows that 5.5 - A = 3.5. So A = 2.

Now we know D = 5.5 + 2 sin[30(t - k)]. We want D to be at its smallest when t = 3. Since sin(t) is minimized when t = -90, we can achieve this by having 30(3 - k) = -90, ie, k = 6.

So D = 5.5 + 2 sin(30(t - 6)). There are several ways of writing this solution, so don't necessarily worry if yours looks different.

Reply 2

MC REN

yeah johnny w is right, (if you check my previous posts this has been covered before)

you could use 270 as well as -90 if you go the other way as well