This question has many parts to it. Its like asking how to build a house and expecting detailied instructions on the building the foundation , the framing and the roof.
It appears that you have a handle on the math part and understand what a sine wave is. So I assume that you can do the math to create an array of X,Y data points of your sine wave as well as the concept of scaling data so that it fits on a graph.
What you need to know is how to create a graphic and display it on a form. Then using those concepts you will take your sinewave data and scale it so that it fits withing the dimensions of your BMP image
Below is some code i had kicking around which creates a BMP (bit map) graphic and displays it in an image box control. you can place the image control within a panel and size the control to match the panel size.
This code will create a new BMP and draw a grid of horizontal and vertical lines. Later you will write code using similar techniques to plot a series of small lines on the BMP that will make your sine wave visible on the graph.
Dim gr As Graphics
Dim sizeX, sizeY, idx, row, rows, col, cols, space As Integer
Dim gryPen As New Pen(Color.Gray, 1)
row = 0
col = 0
sizeX = m_gridBM.Width
sizeY = m_gridBM.Height
rows = 10
space = sizeY / rows
cols = sizeX / space
gr = Graphics.FromImage(m_gridBM)
gr.Clear(Color.Black)
'draw horizontal gradicule lines
gr.DrawLine(gryPen, 0, row, sizeX, row)
For idx = 1 To rows
row = idx * space
If idx = (rows / 2) Then
'make the middle line thicker
gryPen.Width = 3
Else
gryPen.Width = 1
End If
gr.DrawLine(gryPen, 0, row, sizeX, row)
Next
'draw verticle gradicule lines
gr.DrawLine(gryPen, col, 0, col, sizeY)
For idx = 1 To cols
col = idx * space
If idx = (cols / 2) Then
'make the middle line thicker
gryPen.Width = 3
Else
gryPen.Width = 1
End If
gr.DrawLine(gryPen, col, 0, col, sizeY)
Next
With Me.PictureBox1
.Width = sizeX
.Height = sizeY
.Image = m_gridBM
End With
m_gridBM.Save("C:/grid.bmp")
Once you understand how to make a graphic and display it in VB you can move on and learn how to compute a bunch of x,y data points for a Sine wave and scale these points so that they fit onto your BMP grid. Drawing a series of small lines from (X,Y) point to (X,Y) point using a different color and line thickness will display the Sinewave.