F# clarification on creating labels for a pie chart - winforms

Question

I am currently reading Real-World Functional Programming: With Examples in F# and C# by Tomas Petricek and Jon Skeet. I am a bit puzzled by a particular example in which we generate an application that displays a pie chart with some population statistics along with labels.
Now it is the part of drawing the label or rather setting the coordinates of the label that I am confused by. I hope that the author doesn't mind that I attach the excerpt here but it would be hard to get clarification on the code without showing it.
let centerX, centerY = 300.0, 200.0
let labelDistance = 150.0
let drawLabel (gr: Graphics) title startAngle angle =
let lblAngle = float(startAngle + angle / 2)
let ra = Math.PI * 2.0 * lblAngle / 360.0
let x = centerX + labelDistance * cos(ra)
let y = centerY + labelDistance * sin(ra)
let size = gr.MeasureString(title, fnt)
let rc = new PointF(float32(x) - size.Width / 2.0f,
float32(y) - size.Height / 2.0f)
gr.DrawString(title, fnt, Brushes.Black, new RectangleF(rc, size))
It seems that labelDistance and centerX, centerY define some standard "offset" from the center of the drawing surface and I'm guessing that the trigonometric functions define the angle of the label because if I omit those then all labels are placed on top of eachother in the bottom right corner. But I don't quite understand how this works. What exactly happens here?

Answer 1

Giving this a go by adding comments, not necessarily worked out in this order:
// startAngle is the angle in degrees of this segment, angle is the angle of
// the segment itself.
let drawLabel (gr: Graphics) title startAngle angle =
// So this is the angle of the centre of this segment.
let lblAngle = float(startAngle + angle / 2)
// And ra is the same angle, now in radians.
let ra = Math.PI * 2.0 * lblAngle / 360.0
// So these work out the position of the label in the usual
// way, using cosine(angle-in-radians) and then scaling for the X
// and using sine for the Y. Both relative to the centre of the
// circle.
let x = centerX + labelDistance * cos(ra)
let y = centerY + labelDistance * sin(ra)
// How long, in pixels, is the text?
let size = gr.MeasureString(title, fnt)
// Create an instance of the right data structure adjusting
// so the calculated point is the centre of the rectangle
// in which the text will be drawn.
let rc = new PointF(float32(x) - size.Width / 2.0f,
float32(y) - size.Height / 2.0f)
// And, thus, we can now draw the text.
gr.DrawString(title, fnt, Brushes.Black, new RectangleF(rc, size))