C library - casin() function

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The C complex library casin() function operates the complex arcsine of a given complex number. This function is available in C99 and works with complex numbers. Its behavior is completely different from asin(). A asin() function implement the inverse of sine of a number(in radian).

Syntax

Following is the C library syntax of the casin() function −

double complex ccasin(double complex z);

Parameters

It accept only a single parameter z(complex number) which performs the task of arcsine.

Return Value

When no error occurs, the function returns the complex arcsine of z.

Example 1

Following is the C library program that shows the usage of casin() function.

#include <stdio.h>
#include <complex.h>
#include <math.h>

int main() {
   double complex z = 1.0 + 2.0 * I; 
   double complex result = casin(z);
   printf("casin(%lf + %lfi) = %lf + %lfi\n", creal(z), cimag(z), creal(result), cimag(result));
   return 0;
}

Output

On execution of above code, we get the following result −

casin(1.000000 + 2.000000i) = 0.427079 + 1.528571i

Example 2

Here, we demonstrate the series formula of casin to find the number of terms using recursion and display the result with the help of some pre-existing functions such as creal(), cimag(), and cimag().

#include <stdio.h>
#include <complex.h>

double complex casin_recursive(double complex z, int n) {
    if (n == 0) {
        return z;
    }
    double complex term = -(z * z) * (2 * n - 1) / (2 * n) * casin_recursive(z, n - 1);
    return term;
}

int main() {
    double complex z = 1.0 + 2.0 * I; 
    int terms = 10; 
    double complex result = casin_recursive(z, terms);
    printf("casin(%lf + %lfi) = %lf + %lfi (approximated with %d terms)\n", creal(z), cimag(z), creal(result), cimag(result), terms);
    return 0;
}

Output

After executing the above code, we get the following result −

`
casin(1.000000 + 2.000000i) = -1180400.258221 + -3662001.649712i (approximated with 10 terms)