Trigonometry

Recipe	Crates	Categories
Calculate the Side Length of a Triangle
Verify that tan is Equal to sin Divided by cos
Calculate the Distance Between two Points on Earth

Calculate the Side Length of a Triangle

Calculates the length of the hypotenuse of a right-angle triangle with an angle of 2 radians and opposite side length of 80.

fn main() {
    let angle: f64 = 2.0;
    let side_length = 80.0;

    let hypotenuse = side_length / angle.sin();

    println!("Hypotenuse: {}", hypotenuse);
}

Verify that tan is Equal to sin Divided by cos

Verifies tan(x) is equal to sin(x)/cos(x) for x = 6.

fn main() {
    let x: f64 = 6.0;

    let a = x.tan();
    let b = x.sin() / x.cos();

    println!("a: {a}, b: {b}");
    assert_eq!(a, b);
}

Calculate the Distance Between two Points on Earth

By default, Rust provides mathematical float methods⮳ such as trigonometric functions, square root, conversion functions between radians and degrees, and so forth.

The following example computes the distance in kilometers between two points on the Earth with the Haversine⮳ formula. Points are expressed as pairs of latitude and longitude in degrees. Then, to_radians⮳ converts them in radians. sin⮳ cos⮳ powi⮳ and sqrt⮳ compute the central angle. Finally, it's possible to calculate the distance.

fn main() {
    let earth_radius_kilometer = 6371.0_f64;
    let (paris_latitude_degrees, paris_longitude_degrees) =
        (48.85341_f64, -2.34880_f64);
    let (london_latitude_degrees, london_longitude_degrees) =
        (51.50853_f64, -0.12574_f64);

    let paris_latitude = paris_latitude_degrees.to_radians();
    let london_latitude = london_latitude_degrees.to_radians();

    let delta_latitude =
        (paris_latitude_degrees - london_latitude_degrees).to_radians();
    let delta_longitude =
        (paris_longitude_degrees - london_longitude_degrees).to_radians();

    let central_angle_inner = (delta_latitude / 2.0).sin().powi(2)
        + paris_latitude.cos()
            * london_latitude.cos()
            * (delta_longitude / 2.0).sin().powi(2);
    let central_angle = 2.0 * central_angle_inner.sqrt().asin();

    let distance = earth_radius_kilometer * central_angle;

    println!(
        "Distance between Paris and London on the surface of Earth is {:.1} kilometers",
        distance
    );
}