ATN X:

	 10 	REM DEMONSTRATION FOR ATN X
	 20 	REM USING THE 'SERIES GENERATOR'
	 30 	DIM A(12)
	 40 	LET A(1)= -.0000000002
	 50 	LET A(2)=0.0000000010
	 60 	LET A(3)= -.0000000066
	 70 	LET A(4)=0.0000000432
	 80 	LET A(5)= -.0000002850
	 90 	LET A(6)=0.0000019105
	100 	LET A(7)= -.0000131076
	110 	LET A(8)=0.0000928715
	120 	LET A(9)= -.0006905975
	130 	LET A(10)=0.0055679210
	140 	LET A(11)= -.0529464623
	150 	LET A(12)=0.8813735870
	160 	PRINT
	170 	PRINT "ENTER START VALUE"
	180 	INPUT C
	190 	CLS
	200 	PRINT "BASIC PROGRAM", "ROM PROGRAM"
	210 	PRINT "-------------", "-----------"
	220 	PRINT
	230 	FOR J=1 TO 4
	240 	LET B=J*C
	250 	LET D=B
	260 	IF ABS B>=1 THEN LET D= -1/B
	270 	LET Z=2*D*D-1
	280 	LET BREG=12
	290 	REM USE "SERIES GENERATOR"
	300 	GO SUB 550
	310 	LET T=D*T
	320 	IF B > =1 THEN LET T=T+PI/2
	330 	IF B < =-1 THEN LET T=T-PI/2
	340 	PRINT TAB 8;"ATN ";B
	350 	PRINT
	360 	PRINT T,ATN B	(or PRINT T*180/PI,ATN B*180/PI
	370 	PRINT	to obtain the answers in degrees)
	380 	NEXT J
	390 	GO TO 160

NOTES:

  i. When C is entered this program calculates and prints ATN C, ATN (C*2), ATN (C*3)
     and ATN (C*4).
     For a specimen of results, try entering these values: 0.2; -1; 10 and -100. The results
     may be found more interesting if converted to yield degrees by multiplying the
     answers in line 360 by 180/PI.

 ii. The constants A(1) to A(12) in lines 40 to 150 are given (apart from a factor of 1/2)
     in Abramowitz and Stegun Handbook of Mathematical Functions (Dover 1965) page
     82. They can be checked by integrating ATN X/X over the interval U=0 to PI, after
     first multiplying by COS (N*U) for each parameter (i.e. for n=1,2,...,12) and sub-
     stituting COS U=2*X*X-1. Each result should then be divided by PI.