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 |
|
|
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. |