The call type(expr, trig) returns true if expr is a function and the function name is one of the trigonometric functions:

The call type(expr, trig(x)) checks, in addition, that the argument to the trigonometric function contains the variable name x.

The call type(expr, trigh) returns true if expr is a function and the function name is one of the functions:

Otherwise, it returns false.

The call type(expr, trigh(x)) checks, in addition, that the argument to the hyperbolic function contains the variable name x.

It is important to note that the type trigh is a subset of the type trig; that is, objects of type trigh are also of type trig, but the converse is not true.

type/function

$\mathrm{type}\left(\sin \left(x\right)\,'\mathrm{trig}'\right)$

$\mathrm{true}$

$\mathrm{type}\left(\sin \left(x\right)\,'\mathrm{trig}'\right)$

$\mathrm{true}$

$\mathrm{type}\left(\sinh \left(x\right)\,'\mathrm{trigh}'\right)$

$\mathrm{true}$

$\mathrm{type}\left(\sinh \left(x\right)\,'\mathrm{trigh}'\right)$

$\mathrm{true}$

$\mathrm{type}\left(\exp \left(x\right)\,'\mathrm{trig}'\right)$

$\mathrm{false}$

$\mathrm{type}\left(\exp \left(x\right)\,'\mathrm{trigh}'\right)$

$\mathrm{false}$

$\mathrm{type}\left(\sin \left(x\right)+\cos \left(x\right)\,'\mathrm{trig}'\right)$

$\mathrm{false}$

$\mathrm{type}\left(\sin \left(x\right)+\cos \left(x\right)\,'\mathrm{trigh}'\right)$

$\mathrm{false}$

$\mathrm{type}\left(\sin \left(1\right)\,'\mathrm{trig}\left(x\right)'\right)$

$\mathrm{false}$

$\mathrm{type}\left(\sin \left(1\right)\,'\mathrm{trigh}\left(x\right)'\right)$

$\mathrm{false}$

$\mathrm{type}\left(\tanh \left(3x-1\right)\,'\mathrm{trig}\left(x\right)'\right)$

$\mathrm{true}$

$\mathrm{type}\left(\tanh \left(3x-1\right)\,'\mathrm{trigh}\left(x\right)'\right)$

$\mathrm{true}$

$\mathrm{type}\left(\tan \left(3x-1\right)\,'\mathrm{trigh}\left(x\right)'\right)$

$\mathrm{false}$