The atan() Function in Scilab

In Scilab, the atan() function is a powerful tool designed to compute the arctangent of a given number.

atan(x)

Here, 'x' denotes the tangent's value.

The arctangent function provides the angle associated with the specified tangent value, 'x'.

But what is the arctangent? Simply put, it's the inverse trigonometric function of the tangent. It returns the angle corresponding to a specific tangent value. For clarity, the arctangent of the tangent of 'x' is the angle 'x': $$ \text{atan}( \tan(x) ) = x $$ Notably, the atan() function accepts values across the entire real spectrum, delivering results between −π/2 and π/2 radians.

Let's delve into a practical example.

Suppose you're tasked with determining the arctangent of 1 using Scilab.

Input the function: atan(1)

atan(1)

This computation yields the angle in radians that corresponds to a tangent value of 1.

For this specific input, the angle is precisely 0.7853982 radians, equivalent to 45 degrees.

0.7853982

It's crucial to remember that the function's output is in radians. To convert this to degrees, simply multiply the radians by 180 and divide by pi.

0.7853982*180/%pi

45.0

To ensure the accuracy of your result, you can compute the tangent of 0.7853982 radians.

Enter: tan(0.7853982)

tan(0.7853982)

The result? A perfect 1, confirming the accuracy of our earlier computation.

1.0

The atan() function is versatile, allowing for the computation of the arctangent of individual numbers, be they real, complex, or even arrays.

For instance, consider an array of values

A=[0, 0.5, 1, 2]

To compute the arctangent for this array, employ the atan() function.

atan(A)

In this context, the atan() function calculates the arctangent for each array element.

0. 0.4636476 0.7853982 1.1071487

Scilab also introduces a two-parameter variant of the atan() function.

This version accepts y and x coordinates, returning the angle in the Cartesian coordinate system.

atan(x,y)

For illustration, consider a point at coordinates (x;y)=(1,1) on the Cartesian plane.

To determine the arctangent of these coordinates, input: atan(1,1)

atan(1,1)

Consistently, the result is 0.7853982 radians, which translates to 45 degrees.

0.7853982

This dual-parameter iteration is particularly valuable when navigating Cartesian coordinates, especially when pinpointing the angle of a point relative to the x-axis.

In various other programming languages, this function might be recognized as atan2().