This program demonstrates trigonometric functions through interactive graphics, drawing coordinate-plane diagrams that illustrate how SIN, COS, and TAN relate to the four quadrants. It offers a three-option menu: a labeled static quadrant diagram with a drawn unit-circle illustration and BEEP tones, a sample animated parametric plot cycling SIN and COS with user-supplied multipliers, and a Lissajous-style figure generator where the user divides PI by custom degree values for each axis. A custom UDG character “a” is defined at startup via POKEd DATA bytes (0,0,0,255,0,0,0,0), producing a single horizontal midline bar used as a visual separator in the trig-sign labels. The subroutine at line 200 generates an animated star-scatter loading screen using RND-positioned asterisks with descending BEEP tones before drawing a parametric spiral pattern.
Program Analysis
Program Structure
The program is organized into several distinct blocks connected by a central menu at line 20. Execution begins at line 8, initializes the display, calls a UDG setup subroutine at line 1000, then calls an animated intro at line 200 before entering the menu loop.
| Lines | Role |
|---|---|
| 4–8 | REMs and initialization (PAPER, INK, CLS, GO SUB) |
| 10 | GO SUB 1000 — UDG definition |
| 14–16 | Title display and first keypress pause |
| 20–39 | Main menu (options 1–3, input validation) |
| 40–100 | Option 1 — static labeled quadrant/trig diagram with circle and BEEP |
| 200–270 | Animated intro subroutine (star scatter + parametric spiral) |
| 300–370 | Option 2 subroutine — animated parametric ellipse plot (30×SIN, 20×COS) |
| 400–459 | Option 3 entry — user-multiplier parametric plot |
| 460–496 | Axis-drawing sub-block for option 3 |
| 500–560 | PI-divided-by-degrees Lissajous generator |
| 600–660 | Full-parameter Lissajous with user SIN/COS values, step, and PI divisors |
| 1000–1015 | UDG “a” definition via READ/POKE/DATA |
| 9998–9999 | STOP and SAVE |
UDG Definition
The subroutine at line 1000 defines UDG character "a" (char 144) by POKEing 8 bytes read from a DATA statement at line 1010. The data 0,0,0,255,0,0,0,0 produces a single solid horizontal line through the vertical midpoint of the 8×8 cell. This UDG is used repeatedly in lines 57–60 as \a\a\a\a — four consecutive UDGs forming a short horizontal rule separating the sign labels for SIN, COS, and TAN in each quadrant.
Parametric and Lissajous Plotting
The core graphical technique throughout is parametric plotting: a loop variable a drives both X and Y via SIN and COS, producing ellipses or Lissajous figures depending on the PI divisors chosen. Three distinct plotting modes are present:
- Lines 340–360 (subroutine 300): Fixed multipliers —
x=30*SIN(a*PI/180),y=20*COS(a*PI/180)— plotting and drawing from each computed point back to itself, which traces an ellipse. - Lines 410–455 (option 3): User-supplied multipliers
sandcfor SIN and COS respectively, ranging from 1–35 and 1–30. - Lines 500–545 and 600–635: User-supplied PI divisors
d1andd2for SIN and COS independently, enabling true Lissajous figures when the ratiod1/d2is non-unity. The loop runs to 720 (two full cycles) to ensure figure closure.
Bug: Coordinate Multiplication Instead of Addition (Line 535)
Line 535 contains a significant bug: PLOT 128+x,88*y. The Y coordinate uses multiplication (88*y) instead of addition (88+y), as used consistently in every other plotting line (e.g., lines 355, 435, 630). When y is near 1, the plot Y coordinate will be approximately 88, which coincidentally appears correct; however, for any other value of y the plotted point will be wildly wrong or out of range, causing an error or invisible plot.
Bug: Shadowed Loop Variable in Lines 615–635
Lines 615 and 619 both use FOR a=.... The outer loop at line 615 (FOR a=0 TO 360 STEP 3) is immediately superseded by the inner loop at line 619 (FOR a=0 TO 720 STEP s1), since they share the same variable a. The outer loop body never meaningfully iterates — only the axis-drawing at line 617 executes once per outer iteration before the inner loop completes and NEXT a at line 635 terminates the inner loop. The outer NEXT a is never reached, so the outer loop silently runs once and falls through. This is almost certainly unintended.
Navigation and Flow Control
Menu option 3 at line 36 uses GO TO 399, which does not exist as a line number. In Sinclair BASIC, a GO TO targeting a non-existent line transfers control to the next line numerically above the target — in this case line 400, the start of the main parametric program. This is a deliberate memory-saving idiom rather than an error.
After the Lissajous section at line 560, there is no explicit GO TO or RETURN — execution falls through directly into the plot-over-functions block starting at line 600. This means completing the PI-by-degrees section always leads into the more detailed Lissajous entry rather than returning to the menu, unless the user chooses option “a” (repeat) at line 555.
Intro Animation (Lines 200–270)
The subroutine at line 200 uses a FOR x=15 TO 0 STEP -1 loop to scatter asterisks at random screen positions using INT(RND*2-x) for the row and INT(RND*x+x) for the column, accompanied by descending BEEP pitches. It then executes a double-nested loop (lines 208–245) computing r=2-(a*SIN(n/3*PI)) and c=10-(a*COS(n/6*PI)), drawing from a fixed origin at (120,90) to produce a radiating spiral/fan pattern across 13 angular phases (n=0 TO 12).
Key BASIC Idioms
OVER 1in line 61 (and 330, 485) is used inline within aPRINT ATstatement to toggle XOR pixel mode for the axis labels, allowing them to overlap the drawn axes without fully overwriting the graphics.PAUSE 0at lines 16, 365, and 402 halts execution until a key is pressed.- Degree-to-radian conversion is done explicitly as
a*PI/180throughout, since the BASIC trigonometric functions take radians. - Input validation loops (e.g., lines 30, 457, 555, 645) re-prompt by
GO TO-ing back to theINPUTline when the response is out of range.
Content
Image Gallery
Source Code
4 REM 2068 graphics and trig
5 REM by
6 REM Andy Centek Garden City, MI
8 PAPER 0: INK 7: CLS : GO SUB 200
10 GO SUB 1000
14 PRINT AT 2,5;"Trig. affects on graphics."
15 PRINT "Showing plots of trig functions in relation to quadrants."
16 PAUSE 0: CLS
20 CLS : PRINT TAB 14;"MENU"
22 PRINT ''"1-Graph with trig functions"'" labeled on graph."
24 PRINT ''"2-Sample program"
26 PRINT ''"3-Run a program"
28 INPUT n
30 IF n<>1 AND n<>2 AND n<>3 THEN GO TO 28
32 IF n=1 THEN GO TO 40
34 IF n=2 THEN GO SUB 300
36 GO TO 399
39 STOP
40 CLS
44 PLOT 0,88: DRAW 255,0
45 PLOT 128,0: DRAW 0,166
50 PRINT AT 0,12;"Quadrants"
55 PRINT AT 0,6;"II";AT 0,23;"I";AT 21,6;"III";AT 21,23;"IV"
57 PRINT AT 2,5;"+SIN ";AT 3,5;"\a\a\a\a";AT 4,5;"-COS ";AT 3,10;"=-TAN "
58 PAUSE 10: PRINT AT 2,20;"+SIN ";AT 3,20;"\a\a\a\a";AT 3,25;"=+TAN ";AT 4,20;"+COS "
59 PAUSE 10: PRINT AT 17,5;"-SIN ";AT 18,5;"\a\a\a\a";AT 18,10;"=+TAN ";AT 19,5;"-COS "
60 PAUSE 10: PRINT AT 17,20;"-SIN ";AT 18,20;"\a\a\a\a";AT 18,25;"=-TAN ";AT 19,20;"-COS "
61 PRINT AT 21,15;"-Y";AT 1,15;"+Y";AT 10,0; OVER 1;"-X";AT 10,30; OVER 1;"+X"
64 PLOT 128,88: DRAW 40,35: PLOT 128,88: DRAW 30,0: DRAW 0,27
65 PRINT AT 7,20;"S";AT 8,20;"i";AT 9,20;"n"
66 PLOT 128,88: DRAW 42,0: DRAW 0,38
67 PRINT AT 6,22;"T";AT 7,22;"a";AT 8,22;"n"
68 PRINT AT 11,17;"Cos"
69 CIRCLE 128,88,40
70 FOR a=-40 TO 40 STEP 1.25: BEEP .01,-a: BEEP .01,+a: NEXT a
97 INPUT "Enter >>m<< ( ret to menu)";a$
98 IF a$<>"m" THEN GO TO 97
100 GO TO 20
199 STOP
202 PRINT AT 0,4;"Coming up---GRAPHICS "
204 PRINT INVERSE 1;AT 19,0;"I AM COMPUTING--PLEASE WAIT!!"
205 FOR x=15 TO 0 STEP -1: BEEP .01,x: PRINT AT INT (RND*2-x),INT (RND*x+x);"*": NEXT x
206 BRIGHT 1: PAPER 1: INK 7: BORDER 0
208 FOR n=0 TO 12
210 FOR a=0 TO 65 STEP 3
225 LET r=2-(a*SIN (n/3*PI))
230 LET c=10-(a*COS (n/6*PI))
235 PLOT 120,90: DRAW c,r
240 NEXT a
245 NEXT n
250 PRINT INVERSE 1;AT 19,0;" ANDY CENTEK, JR. "
260 PRINT AT 1,5;"*";AT 5,3;"*";AT 10,25;"*";AT 20,7;"*"
270 PAUSE 300: CLS : RETURN
300 REM ** DRAW graph **
305 CLS
310 PLOT 0,88: DRAW 255,0: PLOT 128,0: DRAW 0,166
320 PRINT AT 0,12;"Quadrants"
325 PRINT AT 0,6;"II";AT 0,23;"I";AT 21,6;"III";AT 21,23;"IV"
330 PRINT AT 21,15;"-Y";AT 1,15;"+Y";AT 10,0; OVER 1;"-X";AT 10,30; OVER 1;"+X"
335 PAUSE 100
340 FOR a=0 TO 360 STEP 3
345 LET x=30*SIN (a*PI/180)
350 LET y=20*COS (a*PI/180)
352 PRINT AT 18,5;"X=";INT (x);AT 19,5;"Y=";INT (y)
355 PLOT 128+x,88+y: DRAW x,y
356 PRINT AT 17,20;"A=0 to 360";AT 18,19;"X=20 x SIN A";AT 19,19;"Y=30 x COS A"
357 PAUSE 20: PRINT AT 18,5;"X= ";AT 19,5;"Y= ";
360 NEXT a
365 INPUT "return to menu";a$: PAUSE 0
370 GO TO 20
398 STOP
400 REM ** main program **
401 CLS : PRINT BRIGHT 1;'"Showing the effects of the"'"multipliers of the SIN and COS."
402 PAUSE 0: INPUT "ENTER multipliers, ONE number for the SIN (1 - 35) and ONE forthe COS. (1 - 30)";s,c
404 PAPER 1: INK 7: BORDER 5
405 CLS
406 GO TO 460
410 FOR a=0 TO 360 STEP 3
420 LET y=c*COS (a*PI/180)
430 LET x=s*SIN (a*PI/180)
435 PLOT 128+x,88+y: DRAW x,y
455 NEXT a
456 INPUT "Another or a new program (a or n)?";q$
457 IF q$<>"a" AND q$<>"n" THEN GO TO 456
458 IF q$="a" THEN CLS : GO TO 400
459 GO TO 500
460 REM ** draw graph**
461 CLS
465 PLOT 0,88: DRAW 255,0: PLOT 128,0: DRAW 0,166
475 PRINT AT 0,12;"Quadrants"
480 PRINT AT 0,6;"II";AT 0,23;"I";AT 21,6;"III";AT 21,23;"IV"
485 PRINT AT 21,15;"-Y";AT 1,15;"+Y";AT 10,0; OVER 1;"-X";AT 10,30; OVER 1;"+X"
492 PRINT AT 18,2;s;" x SIN";AT 19,2;c;" x COS";
496 GO TO 410
500 REM ** dividing PI by degrees **
505 CLS
507 PRINT '''"Dividing PI by degrees(0 to 360)";"Input degrees for...";
508 INPUT "SIN ";d1: INPUT ;"COS ";d2
509 CLS : PLOT 0,88: DRAW 255,0: PLOT 128,0: DRAW 0,166
510 FOR a=0 TO 720 STEP 2.5
515 PRINT AT 21,0;"PI/";d1;" SIN - PI/";d2;" COS"
525 LET y=25*COS (a*PI/d2)
530 LET x=35*SIN (a*PI/d1)
535 PLOT 128+x,88*y: DRAW x,y
545 NEXT a
550 INPUT "Another or next program(a/n)?";q$
555 IF q$<>"a" AND q$<>"n" THEN GO TO 550
560 IF q$="a" THEN GO TO 500
600 CLS
605 REM ** plot over functions **
610 PRINT '"Values for SIN and COS."'" Max. SIN Val. = 120"'" Max. COS Val. =80"
611 PRINT '"Dividing PI by degrees (0-360)"
612 INPUT "SIN";s: INPUT "COS";c: INPUT "STEP ";s1: INPUT "SIN PI / degrees";d1: INPUT "COS PI / degrees";d2
613 IF s>120 OR c>80 THEN CLS : PRINT AT 11,13;"TOO BIG !!": GO TO 610
614 CLS : PRINT AT 19,1;s;" x SIN PI/";d1;AT 20,1;c;" x COS PI/";d2;
615 FOR a=0 TO 360 STEP 3
617 PLOT 0,88: DRAW 255,0: PLOT 128,0: DRAW 0,166
619 FOR a=0 TO 720 STEP s1
620 LET y=c*COS (a*PI/d2)
625 LET x=s*SIN (a*PI/d1)
630 PLOT 128+(x/2),88+(y/2): DRAW x/2,y/2
635 NEXT a
640 INPUT "Another or back to menu ?(a/b) ";q$
645 IF q$<>"a" AND q$<>"b" THEN GO TO 640
646 IF q$="a" THEN GO TO 612
660 GO TO 20
1000 REM get line USR a
1002 FOR n=0 TO 7
1004 READ a: POKE USR "a"+n,a
1006 NEXT n
1010 DATA 0,0,0,255,0,0,0,0
1015 RETURN
9998 STOP
9999 SAVE "GrafTrig" LINE 1Note: Type-in program listings on this website use ZMAKEBAS notation for graphics characters.