Trigonometric & Logarithmic Functions

🔺 Trigonometric Functions in C

Trigonometric functions help us deal with angles and measurements in geometry, physics, graphics, and signal processing.

In C, these are provided by the math.h library. They use radians instead of degrees (important!).

✅ Header:

#include <math.h>

🎯 Why radians?

Because C’s math functions are modeled on calculus-based mathematics where radian measure is standard.

📐 Formula:

radians = degrees × (π / 180)

📏 Common Trigonometric Functions

✅ Example:

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

int main() {
    double degrees = 30.0;
    double radians = degrees * (M_PI / 180.0);  // Convert to radians

    printf("sin(30°) = %.2f\\n", sin(radians)); // Should be ~0.5
    printf("cos(30°) = %.2f\\n", cos(radians)); // ~0.866
    printf("tan(30°) = %.2f\\n", tan(radians)); // ~0.577

    return 0;
}

🧠 Did You Know?

• M_PI is defined in math.h (on GNU/Linux or with some compilers). If not, you can define it:

#define M_PI 3.14159265358979323846

⚠️ Warning:

• tan(x) becomes undefined at certain angles like π/2 (90°) or 3π/2 (270°) — it will give huge values or cause runtime errors due to division by zero.

🔍 Inverse Trigonometric Functions

These return the angle when you know the ratio.

✅ Example:

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

int main() {
    double value = 0.5;

    printf("asin(0.5) = %.2f radians\\n", asin(value)); // ≈ 0.52
    printf("acos(0.5) = %.2f radians\\n", acos(value)); // ≈ 1.04
    printf("atan(1) = %.2f radians\\n", atan(1));       // ≈ 0.785

    return 0;
}

📈 Logarithmic Functions in C

Used in:

• Scientific calculations

• Complexity analysis

• Signal strength analysis

• Growth/decay modeling

All logarithmic functions return double and are declared in <math.h>.

🔣 Types of Logarithmic Functions

✅ Example:

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

int main() {
    double num = 1000;

    printf("log10(1000) = %.2f\\n", log10(num));   // 3.0
    printf("log(2.718) = %.2f\\n", log(2.718));    // ~1.0
    printf("exp(2) = %.2f\\n", exp(2));            // ~7.38

    return 0;
}

💥 Common Use-Cases