A sine function has the following key features:

Frequency = 1/8π

Amplitude = 6

Midline: y = 3

y-intercept: (0, 3)

The function is not a reflection of its parent function over the x-axis.

Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.

Try the suggested solution with short explanation; red line means the curve between the first point (on the midline) and the closest maximum; the - - - - line means the curve between the first point (on the midline) and the closest minimum.

Answer Link

ibiscollingwood ibiscollingwood · Answer 2 · 2022-02-11T03:12:38+01:00

The function of sine will be, [tex]y=6sin(\frac{1}{4}x )+3[/tex]

Standard sine function:

It is given as, [tex]y=Asin(wx)+c[/tex]

Where A is amplitude , w is angular frequency.

Given that, A = 5 , frequency [tex]f=\frac{1}{8\pi}[/tex] and y-intercept is (0, 3)

Angular frequency, [tex]w=2\pi f=2\pi *\frac{1}{8\pi} =\frac{1}{4}[/tex]

Substitute y- intercept (0, 3) in standard equation of sine.

[tex]3=6sin(\frac{1}{4}*0 )+c\\\\c=3[/tex]

Thus, Standard equation of sine function will be,

[tex]y=6sin(\frac{1}{4}x )+3[/tex]

The graph of function attached below.

Learn more about Sine function here:

https://brainly.com/question/3522842