a is the amplitude.
b is the frequency.
c is the horizontal shift.
d is the vertical shift.
your equation is y = 3 * sin(x) + 4
the amplitude is 3.
the frequency is 1.
the horizontal shift is 0.
the vertical shift is 4.
here is what the graph of the sine wave looks like.
the horizontal center line of the graph is at y = 0 plus the vertical shift.
tht makes y = 4 the center line of this graph.
the amplitude is the distance between the peak of the graph and the horizontal center line of the graph.
the default amplitude is 1.
when it is 3, the graph goes between y = 4 + 3 and y = 4 - 3 on this graph.
that's y = 7 on the high peak and y = 1 on the low peak.
the frequency of the graph is 1 unless otherwise specified.
the normal period for a sine wave is 360 degrees.
the frequency is 360 divided by the frequency.
here it is 360 / 1 = 360 degrees.
the period of the sine wave is 360 divided by the freuency.
since the frequency is 1, the period is 360 / 1 = 360 degrees.
the default values of y = a * sin(x - c)) + d are:
a = 1
b = 1
c = 0
d = 0
they are implied, if not shown.
for example;
y = sin(x) has a = 1, b = 1, c = 0, and d = 0 implied.
explicitly shown, it would be y = 1 * sin(1 * (x - 0)) + 0.
the domain of the graph is x = - infinity to x = + infinity.
here's a reference from the web.
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,such%20as%20science%20and%20engineering.
here is what several cycles of your sine wave look like.
