cpp_004_Introduction to Math Functions

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C++ provides a wide range of math functions to perform calculations efficiently.

1. Basic Arithmetic Operations

C++ supports standard arithmetic operations such as addition, subtraction, multiplication, and division. 

Code Example:

#include <iostream>
using namespace std;

int main() {
    int a = 10, b = 3;
    cout << "Addition: " << a + b << endl;
    cout << "Subtraction: " << a - b << endl;
    cout << "Multiplication: " << a * b << endl;
    cout << "Division: " << a / b << endl;  // Integer division
    cout << "Modulus: " << a % b << endl;   // Remainder
    return 0;
}

Output:

Addition: 13
Subtraction: 7
Multiplication: 30
Division: 3
Modulus: 1

Explanation:

• Division: Since a and b are integers, the division result is truncated to an integer.
• Modulus: The % operator gives the remainder of the division (10 divided by 3 leaves a remainder of 1).

Explanation:

• Division: Since a and b are integers, the division result is truncated to an integer.
• Modulus: The % operator gives the remainder of the division (10 divided by 3 leaves a remainder of 1).

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2. Trigonometric Functions

Trigonometric functions like sin, cos, and tan are used for angle calculations. M_PI (π) is a predefined constant in <cmath>.

Code Example:

#include <iostream>
#include <cmath>
using namespace std;

int main() {
    double angle = M_PI / 6;  // 30 degrees in radians
    cout << "sin(30°): " << sin(angle) << endl;
    cout << "cos(30°): " << cos(angle) << endl;
    cout << "tan(30°): " << tan(angle) << endl;
    return 0;
}

Output:

sin(30°): 0.5
cos(30°): 0.866025
tan(30°): 0.57735

Explanation:

• Input: The angle is given in radians (not degrees). M_PI/6 corresponds to 30°.
• Outputs: These are the standard trigonometric values for 30°:
• sin(30°) = 0.5
• cos(30°) ≈ 0.866025
• tan(30°) ≈ 0.57735
•  

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3. Explanation of M_PI

M_PI is a predefined constant in <cmath> that represents the value of π (pi) in mathematics. Its approximate value is 3.141592653589793. If M_PI is not available in some environments, you can define it manually:

#define M_PI 3.141592653589793

4. Square Root and Power

The sqrt function calculates the square root, and pow calculates the power of a number.

Code Example:

#include <iostream>
#include <cmath>
using namespace std;

int main() {
    cout << "Square root of 25: " << sqrt(25) << endl;
    cout << "2^5: " << pow(2, 5) << endl;
    return 0;
}

Output:

Square root of 25: 5
2^5: 32

Explanation:

• Square root: sqrt(25) returns 5 because 5×5=25.
• Power: pow(2, 5) returns 32 because 2^5 =2×2×2×2×2.

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5. Rounding Functions

Functions like ceil, floor, round, and trunc handle decimal numbers differently.

Code Example:

#include <iostream>
#include <cmath>
using namespace std;

int main() {
    double num = 7.65;
    cout << "Ceil: " << ceil(num) << endl;   // Rounds up
    cout << "Floor: " << floor(num) << endl; // Rounds down
    cout << "Round: " << round(num) << endl; // Nearest integer
    cout << "Truncate: " << trunc(num) << endl; // Removes fractional part
    return 0;
}

Output:

Ceil: 8
Floor: 7
Round: 8
Truncate: 7

Explanation:

• ceil: Always rounds up (7.65 → 8).
• floor: Always rounds down (7.65 → 7).
• round: Rounds to the nearest integer (7.65 → 8).
• trunc: Removes the fractional part without rounding (7.65 → 7).

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6. Min and Max

The fmin and fmax functions find the smallest and largest of two numbers.

Code Example:

#include <iostream>
#include <cmath>
using namespace std;

int main() {
    double x = 5.7, y = 8.2;
    cout << "Minimum: " << fmin(x, y) << endl;
    cout << "Maximum: " << fmax(x, y) << endl;
    return 0;
}

Output:

Minimum: 5.7
Maximum: 8.2

Explanation:

• fmin: Returns the smaller value.
• fmax: Returns the larger value.

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7. Modulus and Remainder

The fmod function calculates the floating-point remainder, while remainder gives the remainder closest to zero.

Code Example:

#include <iostream>
#include <cmath>
using namespace std;

int main() {
    double num1 = 8.75, num2 = 3.4;
    cout << "fmod(8.75, 3.4): " << fmod(num1, num2) << endl;
    cout << "remainder(8.75, 3.4): " << remainder(num1, num2) << endl;
    return 0;
}

Output:

fmod(8.75, 3.4): 1.95
remainder(8.75, 3.4): -1.45

Explanation:

• fmod: Computes the remainder after division (8.75 - (2 * 3.4) = 1.95).
• remainder: Returns the remainder closest to zero (-1.45). remainder(x,y)=x−(nearest multiple of y)

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8. Infinity and NaN

INFINITY represents positive infinity, and NaN (Not a Number) represents undefined results.

Code Example:

#include <iostream>
#include <cmath>
using namespace std;

int main() {
    cout << "Positive Infinity: " << INFINITY << endl;
    cout << "Negative Infinity: " << -INFINITY << endl;

    double invalid = 0.0 / 0.0;
    cout << "NaN: " << invalid << endl;
    return 0;
}

Output:

Positive Infinity: inf
Negative Infinity: -inf
NaN: nan

Explanation:

• INFINITY: Represents values that exceed the range of floating-point numbers.
• NaN: Results from undefined operations (e.g., dividing 0 by 0).

Conclusion

The functions we covered in this tutorial (like sqrt, pow, fmod, remainder, ceil, floor, etc.) are all part of the C++ Math Library provided in the <cmath> header. These functions help solve common mathematical problems efficiently.

However, the <cmath> library includes many other powerful functions that were not covered here, such as:

• Hyperbolic functions: sinh, cosh, tanh, etc.
• Exponential and logarithmic functions: exp, log, log10, etc.
• Angle conversion: degrees, radians (available in C++20).
• More rounding functions: nearbyint, copysign, etc.

For a complete list of all mathematical functions available in <cmath>, you can refer to the official documentation: