C tan() Function

The tan() function in C is a standard library function that computes the tangent of a given angle. It is part of the C standard library (math.h). This function is useful for performing trigonometric calculations involving angles.

Table of Contents

1. Introduction
2. tan() Function Syntax
3. Understanding tan() Function
4. Examples
   • Computing Tangent of an Angle
   • Using tan() with User Input
5. Real-World Use Case
6. Conclusion

Introduction

The tan() function computes the tangent of a given angle (in radians). The tangent function is a fundamental trigonometric function that returns the ratio of the length of the opposite side to the length of the adjacent side in a right-angled triangle.

tan() Function Syntax

The syntax for the tan() function is as follows:

#include <math.h>
double tan(double x);

Parameters:

• x: The angle in radians for which the tangent is to be computed.

Returns:

• The function returns the tangent of the angle x.

Understanding tan() Function

The tan() function takes an angle in radians as input and returns the tangent of that angle. To convert degrees to radians, use the formula:
[ \text{radians} = \text{degrees} \times \frac{\pi}{180} ]

Examples

Computing Tangent of an Angle

To demonstrate how to use tan() to compute the tangent of an angle, we will write a simple program.

Example

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

int main() {
    double angle = M_PI / 4; // 45 degrees in radians

    // Compute the tangent of the angle
    double tangent_value = tan(angle);

    // Print the result
    printf("Tangent of %.2f radians (45 degrees) is: %.2f\n", angle, tangent_value);

    return 0;
}

Output:

Tangent of 0.79 radians (45 degrees) is: 1.00

Using tan() with User Input

This example shows how to use tan() to compute the tangent of an angle provided by the user.

Example

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

int main() {
    double degrees, radians;

    // Get user input for the angle in degrees
    printf("Enter the angle in degrees: ");
    scanf("%lf", &degrees);

    // Convert degrees to radians
    radians = degrees * (M_PI / 180.0);

    // Compute the tangent of the angle
    double tangent_value = tan(radians);

    // Print the result
    printf("Tangent of %.2f degrees is: %.2f\n", degrees, tangent_value);

    return 0;
}

Output (example user input "45"):

Enter the angle in degrees: 45
Tangent of 45.00 degrees is: 1.00

Real-World Use Case

Calculating the Slope of a Line

In real-world applications, the tan() function can be used to calculate the slope of a line given its angle of inclination.

Example: Calculating the Slope of a Line

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

int main() {
    double angle_degrees, angle_radians, slope;

    // Get user input for the angle of inclination in degrees
    printf("Enter the angle of inclination in degrees: ");
    scanf("%lf", &angle_degrees);

    // Convert angle to radians
    angle_radians = angle_degrees * (M_PI / 180.0);

    // Calculate the slope using the tangent function
    slope = tan(angle_radians);

    // Print the result
    printf("The slope of the line is: %.2f\n", slope);

    return 0;
}

Output (example user input angle "45"):

Enter the angle of inclination in degrees: 45
The slope of the line is: 1.00

Conclusion

The tan() function is essential for computing the tangent of an angle in C. It is useful in various trigonometric calculations, particularly in fields like geometry, physics, and engineering.