asinh() Function

The asinh() function computes the inverse hyperbolic sine of a given value, effectively reversing the hyperbolic sine operation. It is particularly useful in mathematical computations where retrieving the original value from its hyperbolic sine is required.

Syntax of asinh()

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double asinh(double x);

Parameters

ParameterDescription
xValue whose area hyperbolic sine is computed.

Return Value

Returns the area hyperbolic sine of the provided value.

The function typically uses the formula asinh(x) = ln(x + sqrt(x*x + 1)) to perform the computation. It is defined for all real numbers, making it a versatile tool in various mathematical applications involving hyperbolic functions.

Examples for asinh()

Example 1: Computing the Area Hyperbolic Sine for a Positive Value

This example demonstrates how to compute the area hyperbolic sine for a positive value.

Program

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

int main(void) {
    double x = 1.0;
    double result = asinh(x);
    printf("asinh(%.1f) = %f\n", x, result);
    return 0;
}

Explanation:

  1. The program includes the standard libraries required for input-output operations and mathematical functions.
  2. A variable is initialized with a positive value (1.0 in this case).
  3. The asinh() function computes the inverse hyperbolic sine of the value.
  4. The result is printed using printf() to display the computed value.
  5. The program returns 0, indicating successful execution.

Program Output:

asinh(1.0) = 0.881374

Example 2: Computing the Area Hyperbolic Sine for a Negative Value

This example shows how the asinh() function handles negative input values, demonstrating its odd symmetry.

Program

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

int main(void) {
    double x = -1.0;
    double result = asinh(x);
    printf("asinh(%.1f) = %f\n", x, result);
    return 0;
}

Explanation:

  1. The program includes the necessary headers for standard I/O and math operations.
  2. A variable is set to a negative value (-1.0).
  3. The asinh() function computes the inverse hyperbolic sine, correctly handling negative inputs.
  4. The result is printed using printf(), displaying the negative computed value.
  5. The program terminates normally by returning 0.

Program Output:

asinh(-1.0) = -0.881374

Example 3: Evaluating the Area Hyperbolic Sine for a Larger Input Value

This example demonstrates how to evaluate the area hyperbolic sine for a larger input value, illustrating the function’s behavior over an extended range.

Program

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

int main(void) {
    double x = 2.0;
    double result = asinh(x);
    printf("asinh(%.1f) = %f\n", x, result);
    return 0;
}

Explanation:

  1. The standard libraries for input-output and math functions are included at the beginning.
  2. A variable is initialized with a larger positive value (2.0).
  3. The asinh() function calculates the inverse hyperbolic sine for the given input.
  4. The computed result is printed to the console using printf().
  5. The program exits successfully with a return value of 0.

Program Output:

asinh(2.0) = 1.443636