check for inverse trigonometric functions - Maple Help

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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:

arcsin,arccos,arctan,arcsec,arccsc,arccot,arcsinh,arccosh,arctanh,arcsech,arccsch,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:

arcsinh,arccosh,arctanh,arcsech,arccsch,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

typearcsinx,'arctrig'

true

(1)

typearcsinx,'arctrigh'

false

(2)

typearcsinhx,'arctrig'

true

(3)

typearcsinhx,'arctrigh'

true

(4)

typeⅇx,'arctrig'

false

(5)

typeⅇx,'arctrigh'

false

(6)

typearcsinx+arccosx,'arctrig'

false

(7)

typearcsinx+arccosx,'arctrigh'

false

(8)

typearcsin1,'arctrigx'

false

(9)

typearcsin1,'arctrighx'

false

(10)

typearctanh3x1,'arctrigx'

true

(11)

typearctanh3x1,'arctrighx'

true

(12)

See Also

arctrig, type, type/function, type/trig


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