The Arcsine in Scilab

In Scilab, the asin() function serves as the primary trigonometric method to determine the arcsine of a given number.

asin(x)

In this context, `x` denotes the sine value.

The function asin() yields the angle that corresponds to the specified sine value.

But what is the arcsine? It's the inverse function of the sine. Essentially, it returns the angle whose sine is a given value. For clarity, the arcsine of sin(x) is x. $$ \text{asin} ( \sin(x) ) = x $$ The arcsine function accepts values from -1 to 1, the range of the sine, and produces results within the interval from −π/2 to π/2 radians, the domain of the sine.

To illustrate its application in Scilab, consider the following:

Assign the value 0.5 to the variable `x`

x = 0.5

Then, compute the arcsine using the asin(x) function

asin(x)

The resulting arcsine of 0.5 is an angle of 0.5235988 radians, equivalent to 30 degrees.

0.5235988

This specific angle, when its sine is computed, will return a value of 0.5.

To validate this assertion, execute the function sin(0.5235988)

sin(0.5235988)

Indeed, the sine of 0.5235988 radians is 0.5.

0.5

It's imperative to remember that the asin() function's output is consistently in radians.

However, should you require the result in degrees, simply multiply the radian measure by 180 and divide by pi.