SIN X

	 10 	REM DEMONSTRATION FOR SIN X
	 20 	REM USING THE 'SERIES GENERATOR'.
	 30 	DIM A(6)
	 40 	LET A(1)=-.000000003
	 50 	LET A(2)=0.000000592
	 60 	LET A(3)=-.000068294
	 70 	LET A(4)=0.004559008
	 80 	LET A(5)=-.142630785
	 90 	LET A(6)=1.276278962
	100 	PRINT
	110 	PRINT "ENTER START VALUE IN DEGREES"
	120 	INPUT C
	130 	CLS
	140 	LET C=C-10
	150 	PRINT "BASIC PROGRAM","ROM PROGRAM"
	160 	PRINT "-------------","-----------"
	170 	PRINT
	180 	FOR J=1 TO 4
	190 	LET C=C+10
	200! 	LET Y=C/360-INT (C/360+.5)
	210 	LET W=4*Y
	220 	IF W > 1 THEN LET W=2-W
	230 	IF W < -1 THEN LET W=-W-2
	240 	LET Z=2*W*W-1
	250 	LET BREG=6
	260 	REM USE 'SERIES GENERATOR'
	270 	GO SUB 550
	280 	PRINT TAB 6; "SIN ";C;" DEGREES"
	290 	PRINT
	300 	PRINT T*W,SIN (PI*C/180)
	310 	PRINT
	320 	NEXT J
	330 	GO TO 100

NOTES:

  i. When C is entered this program calculates and prints SIN C degrees, SIN (C+10)
     degrees, SIN (C+20) degrees and SIN (C+30) degrees. It also prints the values obtain-
     ed by using the ROM program. For a specimen of results, try entering these values in
     degrees: 0; 5; 100; -80; -260; 3600; -7200.

 ii. The constants A(1) to A(6) in lines 40 to 90 are given (apart from a factor of 1/2) in
     Abramowitz and Stegun Handbook of Mathematical Functions (Dover 1965) page
     76. They can be checked by integrating (SIN (PI*X/2))/X over the interval U=0 to
     PI, after first multiplying by COS (N*U) for each constant (i.e. N=1,2,...,6) and sub-
     stituting COS U=2*X*X-1. Each result should then be divided by PI. (This integra-
     tion can be performed by approximate methods e.g. using Simpson's Rule if there is a
     reasonable computer or programmable calculator to hand.)