feat: add rectangular to polar coordinate conversion (#1003)

Author: AliAlimohammadi

DIRECTORY.md

@@ -83,6 +83,7 @@
     * [Octal to Decimal](https://github.com/TheAlgorithms/Rust/blob/master/src/conversions/octal_to_decimal.rs)
     * [Octal to Hexadecimal](https://github.com/TheAlgorithms/Rust/blob/master/src/conversions/octal_to_hexadecimal.rs)
     * [Order of Magnitude Conversion](https://github.com/TheAlgorithms/Rust/blob/master/src/conversions/order_of_magnitude_conversion.rs)
+    * [Rectangular to Polar](https://github.com/TheAlgorithms/Rust/blob/master/src/conversions/rectangular_to_polar.rs)
     * [RGB-CMYK Conversion](https://github.com/TheAlgorithms/Rust/blob/master/src/conversions/rgb_cmyk_conversion.rs)
     * [RGB-HSV Conversion](https://github.com/TheAlgorithms/Rust/blob/master/src/conversions/rgb_hsv_conversion.rs)
     * [Roman Numerals](https://github.com/TheAlgorithms/Rust/blob/master/src/conversions/roman_numerals.rs)

src/conversions/mod.rs

@@ -13,6 +13,7 @@ mod octal_to_binary;
 mod octal_to_decimal;
 mod octal_to_hexadecimal;
 mod order_of_magnitude_conversion;
+mod rectangular_to_polar;
 mod rgb_cmyk_conversion;
 mod rgb_hsv_conversion;
 mod roman_numerals;
@@ -36,6 +37,7 @@ pub use self::octal_to_hexadecimal::octal_to_hexadecimal;
 pub use self::order_of_magnitude_conversion::{
     convert_metric_length, metric_length_conversion, MetricLengthUnit,
 };
+pub use self::rectangular_to_polar::rectangular_to_polar;
 pub use self::rgb_cmyk_conversion::rgb_to_cmyk;
 pub use self::rgb_hsv_conversion::{hsv_to_rgb, rgb_to_hsv, ColorError, Hsv, Rgb};
 pub use self::roman_numerals::{int_to_roman, roman_to_int};

src/conversions/rectangular_to_polar.rs

@@ -0,0 +1,47 @@
+//! Conversions between rectangular (Cartesian) and polar coordinate systems.
+//!
+//! This module provides utilities for converting rectangular coordinates
+//! into polar coordinates with angles expressed in degrees.
+//!
+//! More information: <https://en.wikipedia.org/wiki/Polar_coordinate_system>
+
+/// Convert rectangular (Cartesian) coordinates to polar coordinates.
+///
+/// The returned tuple contains:
+/// - magnitude (r)
+/// - angle (θ) in degrees
+///
+/// Both values are rounded to 2 decimal places.
+///
+/// # Formula
+/// - r = sqrt(x² + y²)
+/// - θ = atan2(y, x) converted to degrees
+pub fn rectangular_to_polar(real: f64, imag: f64) -> (f64, f64) {
+    let magnitude = (real.powi(2) + imag.powi(2)).sqrt();
+    let angle = imag.atan2(real).to_degrees();
+
+    (
+        round_to_two_decimals(magnitude),
+        round_to_two_decimals(angle),
+    )
+}
+
+fn round_to_two_decimals(value: f64) -> f64 {
+    (value * 100.0).round() / 100.0
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_rectangular_to_polar() {
+        assert_eq!(rectangular_to_polar(5.0, -5.0), (7.07, -45.0));
+        assert_eq!(rectangular_to_polar(-1.0, 1.0), (1.41, 135.0));
+        assert_eq!(rectangular_to_polar(-1.0, -1.0), (1.41, -135.0));
+        assert_eq!(rectangular_to_polar(1e-10, 1e-10), (0.0, 45.0));
+        assert_eq!(rectangular_to_polar(-1e-10, 1e-10), (0.0, 135.0));
+        assert_eq!(rectangular_to_polar(9.75, 5.93), (11.41, 31.31));
+        assert_eq!(rectangular_to_polar(10000.0, 99999.0), (100497.76, 84.29));
+    }
+}