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Yes, but it is called a hyberbolic trigonometric function
TRIGONOMETRIC FUNCTIONS OF ANY ANGLE
It is a trigonometric function. It is also continuous.
The trigonometric function of an angle gives a certain value
The arc trigonometric function of value is simply the angle
For example, if sin (30 degrees) = 0.500
then arc sine ( 0.500) = 30 degrees
An antitrigonometric function is another term for an inverse trigonometric function.