Finding the Inverse Sine of Complex Number in Golang

In mathematics, the inverse sine function, also known as arcsin or sin^-1, is the inverse function of the sine function. It returns the angle whose sine is a given number. The inverse sine function is defined for all real values of y between -1 and 1. When dealing with complex numbers, the inverse sine function is defined for all complex numbers.

In this article, we will discuss how to find the inverse sine of a complex number in Golang using the math/cmplx package.

Syntax

The syntax for finding the inverse sine of a complex number in Golang is −

as := cmplx.Asin(z)

Here, z is the complex number whose inverse sine we want to find, and as is the result.

Example 1: Finding the Inverse Sine of a Complex Number

Let's say we want to find the inverse sine of the complex number z = 3 + 4i. We can do this using the cmplx.Asin function −

package main

import (
   "fmt"
   "math/cmplx"
)

func main() {
   z := complex(3, 4)
   as := cmplx.Asin(z)
   fmt.Println("Inverse Sine of", z, "is", as)
}

Output

Inverse Sine of (3+4i) is (0.6339838656391772+2.3055090312434685i)

Here, we created a complex number z using the complex function, and then found its inverse sine using the cmplx.Asin function.

Example 2: Finding the Inverse Sine of a Real Number

We can also find the inverse sine of a real number using the cmplx.Asin function. To do this, we simply create a complex number with an imaginary part of 0.

package main

import (
   "fmt"
   "math/cmplx"
)

func main() {
   x := 0.5
   z := complex(x, 0)
   as := cmplx.Asin(z)
   fmt.Println("Inverse Sine of", x, "is", as)
}

Output

Inverse Sine of 0.5 is (0.5235987755982989+0i)

Here, we created a complex number z with the real part x and imaginary part 0, and then found its inverse sine using the cmplx.Asin function.

Example 3: Finding the Inverse Sine of a Negative Real Number

We can also find the inverse sine of a negative real number using the cmplx.Asin function. To do this, we create a complex number with the real part as the negative number and the imaginary part as 0.

package main

import (
   "fmt"
   "math/cmplx"
)

func main() {
   x := -0.8
   z := complex(x, 0)
   as := cmplx.Asin(z)
   fmt.Println("Inverse Sine of", x, "is", as)
}

Output

Inverse Sine of -0.8 is (-0.9272952180016123+0i)

Here, we created a complex number z with the real part x and imaginary part 0, and then found its inverse sine using the cmplx.Asin function.

Example 4: Finding the Inverse Sine of a Complex Number with Zero Imaginary Part

Let's now consider a complex number with zero imaginary part and find its inverse sine. We'll use the cmplx.Asin function to do this.

package main

import (
   "fmt"
   "math/cmplx"
)

func main() {
   // Creating a complex number
   z := complex(2, 0)

   // Finding the inverse sine of the complex number
   asin := cmplx.Asin(z)

   // Displaying the result
   fmt.Println("Inverse Sine of", z, "is", asin)
}

Output

Inverse Sine of (2+0i) is (1.5707963267948966+1.3169578969248164i)

In this example, we created a complex number z with a real part of 2 and an imaginary part of 0. We then used the cmplx.Asin function to find its inverse sine. This is equal to π/2, which is the value we would expect for the inverse sine of a real number equal to 1.

Example 5: Finding the Inverse Sine of a Complex Number with Negative Real Part

Let's now consider a complex number with a negative real part and find its inverse sine. We'll use the cmplx.Asin function to do this.

package main

import (
   "fmt"
   "math/cmplx"
)

func main() {
   // Creating a complex number
   z := complex(-3, 4)

   // Finding the inverse sine of the complex number
   asin := cmplx.Asin(z)

   // Displaying the result
   fmt.Println("Inverse Sine of", z, "is", asin)
}

Output

Inverse Sine of (-3+4i) is (-0.6339838656391772+2.3055090312434685i)

Example 6: Finding the Inverse Sine of a Complex Number with Negative Imaginary Part

Let's now consider a complex number with a negative imaginary part and find its inverse sine. We'll use the cmplx.Asin function to do this.

package main

import (
   "fmt"
   "math/cmplx"
)
   
func main() {
   // Creating a complex number
   z := complex(1, -2)
   
   // Finding the inverse sine of the complex number
   asin := cmplx.Asin(z)
   
   // Displaying the result
   fmt.Println("Inverse Sine of", z, "is", asin)
}

Output

Inverse Sine of (1-2i) is (0.42707858639247614-1.528570919480998i)

Conclusion

The inverse sine of a complex number in Golang can be found using the cmplx.Asin function. It takes a complex number as an argument and returns the inverse sine in radians. It is important to note that the returned value will also be a complex number.

In this article, we have discussed the concept of inverse sine, its properties, and the implementation of its calculation using the Golang programming language. We have also covered several examples that demonstrate the use of cmplx.Asin function to find the inverse sine of complex numbers.

It is important to have a clear understanding of complex numbers and their properties before attempting to find their inverse sine. With this knowledge and the implementation details outlined in this article, you should now be able to calculate the inverse sine of complex numbers in your Golang programs.