Time Height above ground
0 45
3 65
6 80
9 85
12 80
15 65
18 45
21 25
24 10
27 5
30 10
33 25
36 45
I know the following things:
The minimum is 5 while the maximum is 85.
amplitude: 85-5/2 = 40
period =360/45 = 8
vertical translation = 5 + 40 = 45
But I can't seem to get the right function for the data above.
To find the function that represents the data points given, you can use a trigonometric function called the sine function. The sine function oscillates between -1 and 1, so by scaling, shifting, and translating the sine function, you can adjust it to fit your data.
To fit the given data points, we can start by using the general form of a sine function: y = A * sin(Bx + C) + D, where A, B, C, and D are constants that we need to determine.
The amplitude of the function is given as 40, which corresponds to half the difference between the maximum and minimum values. Therefore, A = 40.
The period of the function is given as 8. The period is the distance between consecutive peaks or troughs of the function. In this case, the distance between consecutive peaks is 8, so the value B = 2π/8 = π/4.
Next, let's find the vertical translation or the midline of the function. The midline is the average of the maximum and minimum values. In this case, the midline corresponds to a y-value of 45. Therefore, D = 45.
Finally, we need to find the phase shift or horizontal translation of the function. The phase shift is the amount by which the function is shifted horizontally from the standard sine function. In this case, the first point occurs at t = 0, and the standard sine function has its first peak at t = π/2. So, the phase shift is -π/2.
Putting it all together, the function that fits the given data is:
y(t) = 40 * sin((π/4) * t - π/2) + 45
Now, you can use this function to find the corresponding height above the ground for any given time.