add 三角函数

src/algos/math/trigonometry.md

@@ -1 +1,57 @@
-# 三角
+# 三角函数
+
+### 三角形边长计算
+计算角为 2 弧度、对边长度为 80 的直角三角形的斜边长度。
+
+```rust,editable
+fn main() {
+    let angle: f64 = 2.0;
+    let side_length = 80.0;
+
+    let hypotenuse = side_length / angle.sin();
+
+    println!("Hypotenuse: {}", hypotenuse);
+}
+```
+
+### 验证 tan = sin / cos
+
+```rust,editable
+fn main() {
+    let x: f64 = 6.0;
+
+    let a = x.tan();
+    let b = x.sin() / x.cos();
+
+    assert_eq!(a, b);
+}
+```
+
+### 地球上两点间的距离
+下面的代码使用 [Haversine 公式](https://blog.csdn.net/Hardict/article/details/105267473) 计算地球上两点之间的公里数。
+
+```rust,editable
+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
+    );
+}
+```
+