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?

[Kernelpanic]

What do our mathematical specialists think? 

If x < 1, the result cannot be correct because there is an error message. If x > 1 the result is zero.
I should first go through the formula in peace .  . .

[bplus]

When x < 1 do what you did @BSpinoza because even the help says you can't do it with a straight function call. Your solution looks simpler, so if it works, GO FOR IT!

[SMcNeill]

Looks like a glitch to me.

ARCSEC should work in a range from: x ≤ -1 or x ≥ 1

[bplus]

Why is there a forumla for ArcSec given below for Wiki on _ArcSec Keyword?

Something is wrong? a typo a wrong word? something...

Update: Oh that was from old QB stuff, who cares? water under the bridge

[bplus]

Why is there a forumla for ArcSec given below for Wiki on _ArcSec Keyword?

Something is wrong? a typo a wrong word? something...

Update: Oh that was from old QB stuff, who cares? water under the bridge

PRINT _ARCSEC(-2.5) OK it's broken!

[Kernelpanic]

The formula in the wiki seems to be wrong. Is the result of the formula from the QBasic-Manual correct?

Code: (Select All)

Option _Explicit



Dim As Integer x



x = 0

Const PI = 1.141593



'Print _Arcsec(-2.5

Print

Print _Acos(1 / -2.5)

Print

Print ARCSECF(-2.5)



End



Function ARCSECF (x) ' Inverse Secant



  Dim As Double Arcsec



  If x <= 1 Or x >= 1 Then

    Arcsec = Atn(Sqr(x * x - 1)) + Sgn(Sgn(x) - 1) * PI

  Else Beep

  End If

  ARCSECF = Arcsec

End Function

[bplus]

How does BSpinoza's solution look to you, seems like good idea to me.

[Kernelpanic]

Something else comes out of it too. Wait for @Spinoza.

Code: (Select All)

Option _Explicit



Declare Function ARCSECF(x As Integer) As Double



Dim As Integer arcsecw, x



x = -2.5



Const PI = 1.141593



'Print _Arcsec(-2.5

Print

Print _Acos(1 / -2.5)

Print

Print ARCSECF(-2.5)



Print

arcsecw = _Acos(1 / x)

Print arcsecw



End



Function ARCSECF (x As Integer) 'Inverse Secant



  Dim As Double Arcsec



  If x <= 1 Or x >= 1 Then

    Arcsec = Atn(Sqr(x * x - 1)) + Sgn(Sgn(x) - 1) * PI

  Else Beep

  End If

  ARCSECF = Arcsec

End Function

[Kernelpanic]

Correction: @BSpinoza's formula is correct.

Code: (Select All)

Option _Explicit



Declare Function ARCSECF(x As Double) As Double



Dim As Double arcsecw, x



x = -2.5



Const PI = 1.141593



'Print _Arcsec(-2.5

Print

Print _Acos(1 / -2.5)

Print

Print ARCSECF(-2.5)



Print 'Spinoza's Formel

arcsecw = _Acos(1 / x)

Print Using "#.#########"; arcsecw



End