The equation of the water level y, is approximately y=Asin(nt+b).
a) amplitude, A. (1.91m)
b) what is the water level at midnight? (0.95m)
c) Find b to two decimal places.
d) Find n to one decimal place.
1 full wavelength is 12.37hours (given), so 2pi/12.3 = 0.5
At t=0, y=0.95
For C, I can't seem to get the right answer, which is 0.52
So far, so good. You have
y = 1.91 sin(0.5x + b)
But, you want y(0) = 0.95, so
1.91 sin(b) = 0.95
sin(b) = 0.5
b = π/6 = 0.5235
"b) what is the water level at midnight? (0.95m)" is confusing
Is the water level at midnight 0.95 ???
I will assume that is what is meant.
amplitude is 1.91 , so
y= 1.91sin(nt+b)
1 full wavelength is 12.37hours (given), period = 2π/n
2π/n = 12.37
n = 2π/12.37 = .508 , so
y = 1.91sin (.508t + b)
at midnight, t=0, and y = .95
.95 = 1.91sin(.508t + b)
sin(.508(0) + b) = .497382...
b = .52057...
so y = 1.91sin(.508t + .52057)
This is a confusing and poorly worded question.
y = A sin (2 pi t/T + b)
T given as 12.37 ? so 2 pi/T = your n = 0.508
then 2 pi/12.37 = .508
y = 1.91 sin ( .508 t +b)
at t = 0, y = 0.95
0.95 = 1.91 sin b
sin b = 0.497
b = 30 degrees close enough = pi/6 radians = 0.523 radians
(So I agree with your 0.52
now y = 1.91 sin (.508 t + .523)
To find the answer for part (c), which is the value of "b" in the equation y = A*sin(nt+b), we can use the information provided and the known value of y at t=0.
Let's consider the equation y = Asin(nt+b). At t=0, we are given that y=0.95m.
Substituting these values into the equation, we have:
0.95 = A*sin(0+b)
Since sin(0)=0, the equation becomes:
0.95 = Asin(b)
To solve for "b", divide both sides of the equation by "A":
0.95/A = sin(b)
Now, we need to find the inverse sine (also known as arcsine) of the left side of the equation. Use a calculator and
apply the arcsine function to find the value of "b".
b = arcsin(0.95/A)
Given that the amplitude A is 1.91m, substitute this value into the equation:
b = arcsin(0.95/1.91)
Use a calculator to apply the arcsine function to 0.95/1.91 and round the result to two decimal places. This will give you the value of "b" in the equation.
By doing the calculations, we find that b is approximately 0.52.
Therefore, the answer for part (c) is b = 0.52 (rounded to two decimal places).