Math - the Low and High Tides’ Height

Task 2- Part 2

For 19th of September, the low and high tides’ height, and the time period of the tides are not consistent, thus, they need to be averaged to create a function.

Let the model for 19th of September be a Cos graph.

A Cos B(x+C)+D

Average minimum height =0.65m

Average maximum height = 2.56m

Amplitute (A) =   =  = 0.955[pic 1][pic 2]

Average time period between the high and low tides  12hrs 16mins or hrs[pic 3][pic 4]

B= =[pic 5][pic 6]

C →since the model is a Cos graph, max =time at 0000 (12 am)

However, the 1st max occurs at 1112 on the 19th of September.

[pic 7]

D→if f(x)=0.955 Cos x, max = 0.955        min=-0.955

However, in this case, max= 2.56        min=0.65

Differences → max= 2.56-0.955        =1.605        min=0.65+0.955=1.605         

[pic 8]

[pic 9]

, where t = time in 24hrs after the midnight on 19th of September.[pic 10]

One period (T)= max→ D→ min→ D→ max

12hrs 16mins = 3hrs 4mins[pic 11]

There is 3hrs 4mins difference between each point.

Starting from max at 1112,

D       ←       min       ←       D       ←        max      →       D       →       min       →       D       →        max

0200              0504        0808                  1112           1416                    1720               2024          2328

Clarity model: f(t)=A sin ( +B[pic 12]

Write the function in A Cos B(x+C)+D form: A sin +D[pic 13]

A= of the amplitude of [pic 14][pic 15]

  =[pic 16]

D =   =,5[pic 17][pic 18]

= (1.605)[pic 19][pic 20]

If, max=0.955         min=-0.955[pic 21]

However, max=0.546+1.204=1.75     min=-0.546+1.204=0.658[pic 22]

Time period between the high and low tides= = =30hrs[pic 23][pic 24]

One period (T)= D → max → D → min → D

30hrs = 7.5hrs[pic 25]

There is 7.5hrs difference between each point.

Starting from min at 1830,

D       ←                 max               →                D                →               min                →                D      

2000 (18/9)          0330 (19/9)                 1100(19/9)            1830        (19/9)              0200(20/9)

...