C asin() Function

The asin() function computes the inverse sine of a given value and returns the result in radians. It is a fundamental function in trigonometry, serving as the inverse operation of the sine function.

Syntax of asin()

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double asin(double x);

Parameters

ParameterDescription
xInput value in the interval [-1, +1]. Values outside this range will result in a domain error.

Additional Points: The function returns the principal value of the arc sine in the interval [-π/2, +π/2] radians. Note that one radian is equivalent to 180/π degrees. The function expects a value within the specified range; providing a value outside [-1, +1] will trigger a domain error.

Examples for asin()

Example 1: Calculating the Arc Sine of a Positive Value

This example demonstrates how to compute the inverse sine of a positive number within the valid input range.

Program

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

int main() {
    double value = 0.5;
    double result = asin(value);
    
    printf("The arc sine of %.2f is %.2f radians\n", value, result);
    return 0;
}

Explanation:

  1. The program initializes a positive value within the valid range for asin().
  2. The asin() function calculates the inverse sine of the value, returning the result in radians.
  3. The resulting value is printed to the console.

Program Output:

The arc sine of 0.50 is 0.52 radians

Example 2: Calculating the Arc Sine of a Negative Value

This example demonstrates how to compute the inverse sine of a negative value within the acceptable range.

Program

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

int main() {
    double value = -0.5;
    double result = asin(value);
    
    printf("The arc sine of %.2f is %.2f radians\n", value, result);
    return 0;
}

Explanation:

  1. The program initializes a negative value within the valid input range.
  2. The asin() function computes the arc sine of the negative value, returning the result in radians.
  3. The calculated value is displayed using printf().

Program Output:

The arc sine of -0.50 is -0.52 radians

Example 3: Handling the Edge Case with Maximum Valid Input

This example demonstrates the function’s behavior when the input is at the upper limit of the valid range.

Program

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

int main() {
    double value = 1.0;
    double result = asin(value);
    
    printf("The arc sine of %.2f is %.2f radians\n", value, result);
    return 0;
}

Explanation:

  1. The program sets the input value to the maximum valid number, 1.0.
  2. The asin() function computes the arc sine, which should return π/2 radians (approximately 1.57 radians).
  3. The result is printed to verify the output.

Program Output:

The arc sine of 1.00 is 1.57 radians