here's a picture of the graph i generated that looks as close to it as i can manage.
the equation of the graph is, as best i can determine:
y = 2 * sin(2 * (x + 7.239)) + 2
the general form of the equation is:
y = a * sin(b * (x - c)) + d
d = 2 which means the center line of the sine ave is at y = 2.
a = 2 which means that graph extends 2 units above the center line and 2 units below the center line.
b = 2 which means 2 full cycles of the sine wave fit in the normal sine wave cycle of 360 degrees.
this means the period of each sine wave is 180 degrees.
the formula for frequency is f = 360 / p
the formula for period is p = 360 / f
f = frequency
p = period
c = + 7.239 which means the sine wave is shifted to the left 7.239 degrees.
this was most difficult to determine because the picture you were given was not up to any standard of decency that would allow you to find it without having graphing software at your disposal that you were experienced in using.
i was able to find it by playing with the graphing software.
i created the graph of y = sin(x) and then created a line at y = 2.5 and then determined, from the software, that the point where the graph crossed the line at y = 2.5 had an x value of 7.239.
thi meant i had to shift the graph 7.239 degrees to the left.
in order to do that (x - c) became (x + 7.239).
this resulted in the shifting of the graph to the left by 7.239 degrees.
in the graph, y represents the sine wave and x represents the number of degrees.
y is a function of x, so y = f(x) and the equation can be shown as f(x) = as well as y =, although y is used for graphing purposes.
this is difficult to explain, so if you have any questions, feel free to send me an email on anything you might be confused about.
in the meantime, here's a decent reference on the general eqution of a sine wave you might find helpful.
https://mathbitsnotebook.com/Algebra2/TrigGraphs/TGsinusoidal.html#:~:text=A%20sine%20wave%2C%20or%20sinusoid,the%20sine%20function%20in%20trigonometry.&text=(A%20and%20B%20are%20positive).&text=y%20%3D%20A%20sin(Bx),the%20height%20of%20the%20graph.
a complicating factor might be that the reference talks in radians rather than degrees.
keep in mind that the conversion formulas are:
radians = degrees * pi / 180
degrees = radians * 180 / pi
based on this:
180 degrees = 180 * pi / 180 = pi
360 degrees = 360 * pi / 180 = 2 * pi
540 degrees = 540 * pi / 180 = 3 * pi
720 degrees = 720 * pi / 180 = 4 * pi
900 degrees = 900 * pi / 180 = 5 * pi
7.239 degrees = 7.239 * pi / 180 = .1263443846
here's what the same graph i showed you above looks like in radians.
the formula used is y = 2 * (2 * (x + .1263443846) + 2
