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revision 1.47 by jpb, Fri Feb 11 05:44:58 2005 UTC revision 1.48 by jpb, Tue Mar 1 04:53:02 2005 UTC
# Line 18473  With the Inverse flag [@code{arcsincos}] Line 18473  With the Inverse flag [@code{arcsincos}]
18473  vector as an argument and computes @code{arctan2} of the elements.  vector as an argument and computes @code{arctan2} of the elements.
18474  (This command does not accept the Hyperbolic flag.)  (This command does not accept the Hyperbolic flag.)
18475    
18476    @pindex calc-sec
18477    @tindex sec
18478    @pindex calc-csc
18479    @tindex csc
18480    @pindex calc-cot
18481    @tindex cot
18482    @pindex calc-sech
18483    @tindex sech
18484    @pindex calc-csch
18485    @tindex csch
18486    @pindex calc-coth
18487    @tindex coth
18488    The remaining trigonometric functions, @code{calc-sec} [@code{sec}],
18489    @code{calc-csc} [@code{csc}] and @code{calc-sec} [@code{sec}], are also
18490    available.  With the Hyperbolic flag, these compute their hyperbolic
18491    counterparts, which are also available separately as @code{calc-sech}
18492    [@code{sech}], @code{calc-csch} [@code{csch}] and @code{calc-sech}
18493    [@code{sech}].  (These commmands do not accept the Inverse flag.)
18494    
18495  @node Advanced Math Functions, Branch Cuts, Trigonometric and Hyperbolic Functions, Scientific Functions  @node Advanced Math Functions, Branch Cuts, Trigonometric and Hyperbolic Functions, Scientific Functions
18496  @section Advanced Mathematical Functions  @section Advanced Mathematical Functions
18497    
# Line 22730  declared to be an integer. Line 22749  declared to be an integer.
22749  \bigskip  \bigskip
22750  @end tex  @end tex
22751    
22752  Trigonometric functions are simplified in several ways.  First,  Trigonometric functions are simplified in several ways.  Whenever a
22753  @expr{@tfn{sin}(@tfn{arcsin}(x))} is simplified to @expr{x}, and  products of two trigonometric functions can be replaced by a single
22754  similarly for @code{cos} and @code{tan}.  If the argument to  function, the replacement is made; for example,
22755  @code{sin} is negative-looking, it is simplified to  @expr{@tfn{tan}(x) @tfn{cos}(x)} is simplified to @expr{@tfn{sin}(x)}.
22756  @expr{-@tfn{sin}(x),},  and similarly for @code{cos} and @code{tan}.  Reciprocals of trigonometric functions are replaced by their reciprocal
22757  Finally, certain special values of the argument are recognized;  function; for example, @expr{1/@tfn{sec}(x)} is simplified to
22758  @pxref{Trigonometric and Hyperbolic Functions}.  @expr{@tfn{cos}(x)}.  The corresponding simplifications for the
22759    hyperbolic functions are also handled.
22760    
22761    Trigonometric functions of their inverse functions are
22762    simplified. The expression @expr{@tfn{sin}(@tfn{arcsin}(x))} is
22763    simplified to @expr{x}, and similarly for @code{cos} and @code{tan}.  
22764  Trigonometric functions of inverses of different trigonometric  Trigonometric functions of inverses of different trigonometric
22765  functions can also be simplified, as in @expr{@tfn{sin}(@tfn{arccos}(x))}  functions can also be simplified, as in @expr{@tfn{sin}(@tfn{arccos}(x))}
22766  to @expr{@tfn{sqrt}(1 - x^2)}.  to @expr{@tfn{sqrt}(1 - x^2)}.
22767    
22768    If the argument to @code{sin} is negative-looking, it is simplified to
22769    @expr{-@tfn{sin}(x)}, and similarly for @code{cos} and @code{tan}.
22770    Finally, certain special values of the argument are recognized;
22771    @pxref{Trigonometric and Hyperbolic Functions}.
22772    
22773  Hyperbolic functions of their inverses and of negative-looking  Hyperbolic functions of their inverses and of negative-looking
22774  arguments are also handled, as are exponentials of inverse  arguments are also handled, as are exponentials of inverse
22775  hyperbolic functions.  hyperbolic functions.

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