The asec() Function in Scilab

Scilab provides a powerful function, asec(), designed to compute the arcsecant.

asec(x)

Here, 'x' represents the secant value for which you're aiming to determine the corresponding angle.

The arcsecant function, in essence, gives back the magnitude of an angle, measured in radians, that matches the given x value in the secant.

So, what exactly is the arcsecant? It stands as the inverse trigonometric counterpart of the secant, denoted as sec(). Mathematically, this relationship is captured by the equation: $$ x = \text{arcsec}( \sec(x) ) $$ Another representation can be: $$ \text{asec}(x) = \text{arccos} ( \frac{1}{x} ) $$

To better understand, let's delve into a hands-on example.

Suppose we want to calculate the arcsecant of 10.

arcsec(10)

This calculation reveals that the arcsecant of 10 is equivalent to an angle measuring 1.4706289 radians.

ans=
1.4706289

Interestingly, this is the exact angle you would introduce into the sec() function to retrieve a value of 10.

For verification purposes, input sec(1.4706289)

sec(1.4706289)

The outcome? Approximately 10.

ans=
9.9999994

It's worth noting that the result isn't a perfect 10 due to the utilization of a truncated number, 1.4706289, rounded to the eighth decimal place.

For precision's sake, using the exact result from asec(10) would yield a perfect 10.

sec(asec(10))

ans=
10.