arctrig - Maple Help

type/arctrig

check for inverse trigonometric functions

type/arctrigh

check for inverse hyperbolic functions

 Calling Sequence type(expr, arctrig) type(expr, arctrig(x)) type(expr, arctrigh) type(expr, arctrigh(x))

Parameters

 expr - any expression x - variable name

Description

 • The call type(expr, arctrig) returns true if expr is a function and the function name is one of the inverse trigonometric or hyperbolic functions:

$\mathrm{arcsin},\mathrm{arccos},\mathrm{arctan},\mathrm{arcsec},\mathrm{arccsc},\mathrm{arccot},\mathrm{arcsinh},\mathrm{arccosh},\mathrm{arctanh},\mathrm{arcsech},\mathrm{arccsch},\mathrm{arccoth}$

 • The call type(expr, arctrig(x)) checks, in addition, that the argument to the inverse trigonometric function contains the variable name x.
 • The call type(expr, arctrigh) returns true if expr is a function and the function name is one of the inverse hyperbolic functions:

$\mathrm{arcsinh},\mathrm{arccosh},\mathrm{arctanh},\mathrm{arcsech},\mathrm{arccsch},\mathrm{arccoth}$

 • The call type(expr, arctrigh(x)) checks, in addition, that the argument to the inverse hyperbolic function contains the variable name x.
 • Note that the arctrigh type is a subset of the arctrig type, in the sense that an expression of type arctrigh is also of type arctrig. However, the converse is not true: the arcsin function is of type arctrig but not of type arctrigh.

Examples

 > $\mathrm{type}\left(\mathrm{arcsin}\left(x\right),'\mathrm{arctrig}'\right)$
 ${\mathrm{true}}$ (1)
 > $\mathrm{type}\left(\mathrm{arcsin}\left(x\right),'\mathrm{arctrigh}'\right)$
 ${\mathrm{false}}$ (2)
 > $\mathrm{type}\left(\mathrm{arcsinh}\left(x\right),'\mathrm{arctrig}'\right)$
 ${\mathrm{true}}$ (3)
 > $\mathrm{type}\left(\mathrm{arcsinh}\left(x\right),'\mathrm{arctrigh}'\right)$
 ${\mathrm{true}}$ (4)
 > $\mathrm{type}\left(\mathrm{exp}\left(x\right),'\mathrm{arctrig}'\right)$
 ${\mathrm{false}}$ (5)
 > $\mathrm{type}\left(\mathrm{exp}\left(x\right),'\mathrm{arctrigh}'\right)$
 ${\mathrm{false}}$ (6)
 > $\mathrm{type}\left(\mathrm{arcsin}\left(x\right)+\mathrm{arccos}\left(x\right),'\mathrm{arctrig}'\right)$
 ${\mathrm{false}}$ (7)
 > $\mathrm{type}\left(\mathrm{arcsin}\left(x\right)+\mathrm{arccos}\left(x\right),'\mathrm{arctrigh}'\right)$
 ${\mathrm{false}}$ (8)
 > $\mathrm{type}\left(\mathrm{arcsin}\left(1\right),'\mathrm{arctrig}\left(x\right)'\right)$
 ${\mathrm{false}}$ (9)
 > $\mathrm{type}\left(\mathrm{arcsin}\left(1\right),'\mathrm{arctrigh}\left(x\right)'\right)$
 ${\mathrm{false}}$ (10)
 > $\mathrm{type}\left(\mathrm{arctanh}\left(3x-1\right),'\mathrm{arctrig}\left(x\right)'\right)$
 ${\mathrm{true}}$ (11)
 > $\mathrm{type}\left(\mathrm{arctanh}\left(3x-1\right),'\mathrm{arctrigh}\left(x\right)'\right)$
 ${\mathrm{true}}$ (12)