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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 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(1+COS Y) to obtain TAN (Y/2) and hence (using ATN) Y/2 and finally Y.
Input
Output
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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