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In a fresh MACSYMA, type control-^ to quit into LISP.
(CDR '%SIN) will show you a property of $INVERSE with value %ASIN.
Type (FASLOAD SOLVE FASL DSK MACSYM).  (CDR '%SIN) shows you that 
the property is now ADISPLINE, a function in SOLVE, rather than 
$INVERSE.  Fasloading in other files instead of SOLVE FASL clobbers 
the property list of %SIN (and %COS, etc., wherever "$INVERSE" appears) 
in other similar ways.  $INVERSE is a purified property.