How to get the amplitud , period and those values. And if i have to find the average why and how?

One researcher gathered the following tidal data at Bondi Beach on Monday 24/02/2020 and Tuesday 25/02/2020.

1. (a) Graph the data neatly from the table, giving the tide height h as a function of time t, where time is measured in hours after midnight at the beginning of Monday 24/02/2020. Place an approximate sinusoidal curve through the points.

2. (b) Find a formula y = h(t) = d+A sin [k (t )] which approximately models the tide height, where, as in part a), t is measured in hours after midnight at the beginning of the Monday. For this you will need to caclulate the following (where you may round your calculations to 2 decimal places):

   1. (i) An approximation of the amplitude A. Use all values given in the table.

   2. (ii) An approximation of the mean value d. Use all values given in the table.

   3. (iii) An approximation for the period p, by calculating the time between each successive low tide and then high tide first. Use all values given in the table.

   4. (iv) An approximation for the horizontal shift , by using y = h(t) = d + Asin[k(t)] with the values for A, d and p found above and only the first low tide value given.

3. (c) Plot or sketch a neat and accurate graph of y = h(t) over the first 24 hours, starting at t = 0. Clearly indicate the maximum and minimum values, as well as the displacement when t = 0.

4. (d) According to the model y = h(t) what is the predicted high tide water depth in the afternoon of Tuesday 03/03/2020?

5. (e) Use the WillyWeather website to find the actual value for the high tide water depth in the afternoon of Tuesday 03/03/2020 and make some brief comment about any differences.

Date Time Height (m) | High Low 24/02/2020 3:31 a.m. 0.53 T L 24/02/2020 | 9:56 a.. | 176 | H . 24/02/2020 4:21 p.m. 0.42 T L 24/02/2020 | 10:22 p.m. 1.47 25/02/2020 4:09 a.m. 0.53 25/02/2020 10:29 a.m. 1.72 H H Date Time Height (m) | High Low 24/02/2020 3:31 a.m. 0.53 T L 24/02/2020 | 9:56 a.. | 176 | H . 24/02/2020 4:21 p.m. 0.42 T L 24/02/2020 | 10:22 p.m. 1.47 25/02/2020 4:09 a.m. 0.53 25/02/2020 10:29 a.m. 1.72 H H