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Introduction to BASIC Foundation of Graphics
Set up the Coordinate System
First, set up the coordinate system with a SET WINDOW statement.
The meaning of four parameters of a SET WINDOW statement is as follows.
SET WINDOW left , right , bottom , top
Example.
`SET WINDOW -4,4,0,8`
The range of x coordinate and y coordinate are set to be -4～4 and 0～8, respectively.
[Note]
Ordinary, the drawing pane is square.
If you want to draw correct figures, set the coordinate system so that right - left = top - bottom.
Draw the axes
`DRAW AXES`
draws the axes with ticks.
`DRAW GRID`
draws the coordinate grid.
`DRAW axes(x,y)`
draws the axes with tick intervals x, y.
`DRAW grid(x,y)`
draws the grid with intervals x, y.

Draw curves
Use PLOT LINES statements to draw curves.
The principle of drawing a curve resembles that of a XY-plotter.
Lines or curves are drawn by a pen.
When the pen moves if it is down, a line or curve is drawn.
When the pen moves if it is up, none are drawn.
PLOT LINES: x, y
moves to the point (x, y) and makes the pen up.
PLOT LINES: x,y;
moves to the point (x, y) and makes the pen down.
PLOT LINES
makes the pen up.
The initial pen state is up.
Example.
(1) A program which draws a graph of a function.

    10 DEF f(x)=x^3+2*x+1
    20 SET WINDOW -5,5,-5,5
    30 DRAW grid
    40 FOR x=-5 TO 5 STEP 0.01
    50     PLOT LINES: x,f(x);
    60 NEXT x
    70 END

(2) A program which draws two or more curves.

    10  SET WINDOW -5,5,-5,5
    20  FOR x=-5 TO 5 STEP 0.01
    30     PLOT LINES: x, sin(x);
    40  NEXT x
    50  PLOT LINES
    60  FOR x=-5 TO 5 STEP 0.01
    70      PLOT LINES: x,cos(x);
    80  NEXT x
    90  END

The PLOT LINES in line 50 is necessary for disconnecting the curves.
(3) A curve of parametric equation.

    10 option angle degrees
    20 SET WINDOW -4,4,-4,4
    30 DRAW axes
    40 FOR t=0 TO 360
    50     PLOT LINES: 3*cos(t),2*sin(t);
    60 NEXT t
    70 END

(4) A curve defined in the polar coordinate.

    10 SET WINDOW -2,2,-2,2
    20 DRAW axes
    30 FOR t=0 TO 2*pi STEP pi/180
    40     LET r=1+cos(t)
    50     PLOT LINES: r*cos(t),r*sin(t);
    60 NEXT t
    70 END

[Supplement]
To convert the rectangular coordinates to the polar coordinates, execute

      LET r=SQR(x^2+y^2)
      LET t=ANGLE(x,y)