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14387: THE 'ARCSIN' FUNCTION (offset 34)
The address of this routine is found in the table of addresses. It is called via the calculator literal 34 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 14387 RST 40 X
14388 DEFB 49 duplicate: X, X
14389 DEFB 49 duplicate: X, X, X
14390 DEFB 4 multiply: X, X*X
14391 DEFB 161 stk_one: X, X*X, 1
14392 DEFB 3 subtract: X, X*X-1
14393 DEFB 27 negate: X, 1-X*X
14394 DEFB 40 sqr: X, SQR (1-X*X)
14395 DEFB 161 stk_one: X, SQR (1-X*X), 1
14396 DEFB 15 addition: X, 1+SQR (1-X*X)
14397 DEFB 5 division: X/(1+SQR (1-X*X))=TAN (Y/2)
14398 DEFB 36 atn: Y/2
14399 DEFB 49 duplicate: Y/2, Y/2
14400 DEFB 15 addition: Y=ASN X
14401 DEFB 56 end_calc
14402 RET Finished: 'last value'=ASN X.
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