Scilab's sec() Function

In Scilab, the sec() function is designed to compute the secant of a given angle.

sec(x)

In this context, 'x' denotes an angle measured in radians.

The sec() function efficiently calculates the secant for the specified angle x.

But what is the secant function? At its core, it's a trigonometric function representing the reciprocal of an angle's cosine. Represented mathematically, it's given by: $$ \sec(x) = \frac{1}{\cos(x)} $$ The function's range spans real numbers between (-∞,1)∪(1,∞).

Let's delve into a hands-on example.

Assign a value in radians to the variable 'x', which will represent our angle's measure.

Consider an angle of π/4 radians for this demonstration.

x = %pi/4;

Here, the constant %pi stands for the value of pi (π) within Scilab.

Now, evaluate the function using sec(x):

sec(x)

For an angle of π/4 radians, the secant value is 1.4142136

1.4142136

Interestingly, this matches the result you'd achieve by determining the reciprocal of the cosine, 1/cos(x).

1/cos(x)

ans=
1.4142136

To visualize the secant function, employ the following command sequence:

clf
x = linspace(-1, 1, 100);
y = sec(x * %pi);
xlabel('x (radiant)');
ylabel('sec(x)');
title('Sec');
plot(x, y);

Executing this will prompt Scilab to render a graph of the function, spanning from -π to +π radians.

In conclusion, it's worth noting that Scilab also provides the arcsecant function, termed asec(), which serves as the inverse of the secant.