Draw n-gon problem

Function poly_radius#(sidelength:Float,num_sides:Float)
		Local r:Float = sidelength /(2.0*Sin(180.0/num_sides))
		Return r
End Function

Function draw_ngon(x#,y#,numsides%,sidelength#)
	Local small_angle# =360.0/Float(numsides)
	Local start_angle#=0
	Local radius#=poly_radius(sidelength,numsides)
	
		For Local i=0 To numsides-1
		DrawLine x+Sin(start_angle)*radius,y-Cos(start_angle)*radius,x+Sin(start_angle+small_angle)*radius,y-Cos(start_angle+small_angle)*radius 
		start_angle:+small_angle
		Next
		Flip
		
End Function

Graphics 640,480
draw_ngon 100,100,16,32
While Not KeyHit(KEY_ESCAPE)
Wend

Two things:
You're drawing one too many sides.

You're also depending upon multiplications to work out points, which generally is a bad idea. Depending upon the floating point errors, you'll overshoot or undershoot the final value. Accumulate the starting angle, rather than calculating it.