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3833: THE 'ARCSIN' FUNCTION (offset +22)
 The address of this routine is found in the table of addresses. It is called via the calculator literal +22 by the routine at acs. It is also called indirectly via fp_calc_2. This subroutine handles the function ASN X and returns a real number from -π/2 to π/2 inclusive which is equal to the value in radians of the angle whose sine is X. Thereby if Y=ASN X then X=SIN Y. This subroutine uses the trigonometric identity TAN (Y/2)=SIN Y/(1+COS Y) to obtain TAN (Y/2) and hence (using ATN) Y/2 and finally Y. asn 3833 RST \$28 X 3834 DEFB \$31 duplicate: X, X 3835 DEFB \$31 duplicate: X, X, X 3836 DEFB \$04 multiply: X, X*X 3837 DEFB \$A1 stk_one: X, X*X, 1 3838 DEFB \$03 subtract: X, X*X-1 3839 DEFB \$1B negate: X, 1-X*X 383A DEFB \$28 sqr: X, SQR (1-X*X) 383B DEFB \$A1 stk_one: X, SQR (1-X*X), 1 383C DEFB \$0F addition: X, 1+SQR (1-X*X) 383D DEFB \$05 division: X/(1+SQR (1-X*X))=TAN (Y/2) 383E DEFB \$24 atn: Y/2 383F DEFB \$31 duplicate: Y/2, Y/2 3840 DEFB \$0F addition: Y=ASN X 3841 DEFB \$38 end_calc 3842 RET Finished: 'last value'=ASN X.
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