function "_ARCSEC()" is wrong?

[BSpinoza]

One example:

Code: (Select All)

PRINT _ARCSEC(-2.5)

results in "illegal function call".

But " .... the domain of sec inverse x is (-∞, -1] U [1, ∞) (being the range of secant function) and the range of arcsec is [0, π/2) U (π/2, π] (principal branch of sec x). ..."

From: https://www.cuemath.com/trigonometry/sec-inverse-x/

The result should be 1.982313172862385.

An alternative formula gives the correct result:

arcsec(x) = acos(1/x)

Code: (Select All)

PRINT _ACOS(1/-2.5)

This works fine and delivers: 1.982313172862385. 

The Help says:

  FUNCTION ARCSEC (x) ' Inverse Secant
    IF x < 1 THEN ARCSEC = ATN(x / SQR(1 - x * x)) + (SGN(x) - 1) * (2 * ATN(1)) ELSE BEEP
END FUNCTION

 I think this is not correct!   

 Correct for the domain is:  |x| > 1 

What do our mathematical specialists think?