The acos() function within Scilab

In Scilab, the acos() function is crafted to compute the arccosine.

acos()

The parameter `x` can be either a singular number or an array of numbers. In the case of an array, the function computes the arccosine for each individual element.

The arccosine function yields the amplitude of the angle that defines the cosine value.

But what is arccosine? Simply put, arccosine is the inverse of the cosine function. It's a trigonometric function that provides the angle for a given cosine value. This means if you have the value of the cosine, the arccosine can be used to determine the corresponding angle. For instance, the arccosine of cos(x) is `x`. $$ \text{acos} ( \cos(x) ) = x $$ The arccosine function accepts values ranging from -1 to 1, the codomain of cosine, and produces results within the range of −π/2 to π/2 radians, the domain of cosine.

To illustrate with a practical example

Suppose you aim to compute the arccosine of 0.5 using Scilab.

Firstly, assign the value 0.5 to the variable `x`:

x = 0.5

Then, compute the arccosine with the acos(x) function.

acos(x)

This computation yields 1.0471976 radians, equivalent to 60 degrees.

1.0471976

To verify the accuracy of this calculated angle, compute the cosine of 1.0471976.

Input cos(1.0471976) and execute.

cos(1.0471976)

The output, 0.5, affirms that the arccosine of 0.5 is indeed 1.0471976 radians.

0.5

For those who favor degrees over radians, the result can be converted by multiplying the radians by the factor of 180 divided by pi.