sketching tide functions
Given a set date from teh calender and a starting time
How do you equate the tides for a 24-hour period after this time and date to an equation of the form y=a cos b(x-c)+d. I know the answer should include a sketch of the function, where teh x-axis represents time in hours (0<t<24) and I am given the starting time t=0
The low tides are:
So the high tide is 3.75 m and the low tide is 0.69m
If you can help that'd be great thanx
1. Convert the times to decimal hours from 00:00.
Originally Posted by needmathshelp
2. The maximum of your model of tide height y=a cos b(x-c)+d is
a+d, and the mimium is -a+d as the maximum and minimum of cos
are +1 and -1. Set these equal to the average high and low tides
a+d = (3.52+3.96)/2 = 3.75
-a+d=(0.67+0.71)/2 = 0.69.
Use these to solve for a and d.
3 The interval t between the maximum and minimum of the model is:
t = 2 pi/b,
b = 2 pi / t,
so now compute the mean time between the high and low and low and
high tides and use that to solve for b.
4. The first maximum of the model occurs at 08:40, and this corresponds
to x-c=0, (where x is the time in decimal hours corresponding to 08:40),