Python math三角函数详解 - sin/cos/tan与反三角函数使用指南

import math

# 基本三角函数
math.sin(x)       # 正弦
math.cos(x)       # 余弦
math.tan(x)       # 正切

# 反三角函数
math.asin(x)      # 反正弦，x ∈ [-1, 1]
math.acos(x)      # 反余弦，x ∈ [-1, 1]
math.atan(x)      # 反正切
math.atan2(y, x)  # 双参数反正切（推荐）

# 角度与弧度转换
math.degrees(x)   # 弧度 → 角度
math.radians(x)   # 角度 → 弧度

# 双曲函数
math.sinh(x)      # 双曲正弦
math.cosh(x)      # 双曲余弦
math.tanh(x)      # 双曲正切

import math

# 角度转弧度
angle = 30
rad = math.radians(angle)
print(f"{angle}度 = {rad:.4f}弧度")

# 三角函数
print(f"sin(30°) = {math.sin(rad):.4f}")
print(f"cos(30°) = {math.cos(rad):.4f}")
print(f"tan(30°) = {math.tan(rad):.4f}")

# 特殊角度
print(f"\nsin(0°)  = {math.sin(0):.4f}")
print(f"cos(0°)  = {math.cos(0):.4f}")
print(f"sin(90°) = {math.sin(math.radians(90)):.4f}")
print(f"cos(90°) = {math.cos(math.radians(90)):.6f}")  # 接近0

# 弧度转角度
print(f"\nπ弧度 = {math.degrees(math.pi):.1f}度")
print(f"2π弧度 = {math.degrees(2 * math.pi):.1f}度")

# 输出：
# 30度 = 0.5236弧度
# sin(30°) = 0.5000
# cos(30°) = 0.8660
# tan(30°) = 0.5774
#
# sin(0°)  = 0.0000
# cos(0°)  = 1.0000
# sin(90°) = 1.0000
# cos(90°) = 0.000000
#
# π弧度 = 180.0度
# 2π弧度 = 360.0度

import math

# 已知直角三角形边长，求角度
opposite = 3   # 对边
adjacent = 4   # 邻边
hypotenuse = 5 # 斜边

# 使用 asin 求角
angle_rad = math.asin(opposite / hypotenuse)
angle_deg = math.degrees(angle_rad)
print(f"asin(3/5) = {angle_deg:.1f}°")

# 使用 acos 求角
angle_rad2 = math.acos(adjacent / hypotenuse)
print(f"acos(4/5) = {math.degrees(angle_rad2):.1f}°")

# 使用 atan 求角
angle_rad3 = math.atan(opposite / adjacent)
print(f"atan(3/4) = {math.degrees(angle_rad3):.1f}°")

# atan2 计算方位角（推荐）
points = [(1, 0), (1, 1), (0, 1), (-1, 1), (-1, 0), (-1, -1), (0, -1), (1, -1)]
print("\n各点的方位角:")
for x, y in points:
    angle = math.degrees(math.atan2(y, x))
    print(f"  ({x:2d},{y:2d}) -> {angle:7.1f}°")

# 输出：
# asin(3/5) = 36.9°
# acos(4/5) = 36.9°
# atan(3/4) = 36.9°
#
# 各点的方位角:
#   ( 1, 0) ->     0.0°
#   ( 1, 1) ->    45.0°
#   ( 0, 1) ->    90.0°
#   (-1, 1) ->   135.0°
#   (-1, 0) ->   180.0°
#   (-1,-1) ->  -135.0°
#   ( 0,-1) ->   -90.0°
#   ( 1,-1) ->   -45.0°

import math

# 圆周运动：计算物体在圆上的位置
radius = 10
print("圆周运动位置:")
for angle_deg in range(0, 361, 45):
    rad = math.radians(angle_deg)
    x = radius * math.cos(rad)
    y = radius * math.sin(rad)
    print(f"  {angle_deg:3d}°: ({x:7.2f}, {y:7.2f})")

# 坐标旋转：将点(x, y)绕原点旋转angle度
def rotate_point(x, y, angle_deg):
    """将点(x, y)绕原点旋转指定角度"""
    rad = math.radians(angle_deg)
    new_x = x * math.cos(rad) - y * math.sin(rad)
    new_y = x * math.sin(rad) + y * math.cos(rad)
    return new_x, new_y

# 旋转点 (3, 4) 90度
point = (3, 4)
for angle in [0, 90, 180, 270]:
    rotated = rotate_point(point[0], point[1], angle)
    print(f"\n({point[0]},{point[1]}) 旋转{angle}° -> ({rotated[0]:.2f}, {rotated[1]:.2f})")

# 输出：
# 圆周运动位置:
#     0°: (  10.00,   0.00)
#    45°: (   7.07,   7.07)
#    90°: (   0.00,  10.00)
#   135°: (  -7.07,   7.07)
#   180°: ( -10.00,   0.00)
#   225°: (  -7.07,  -7.07)
#   270°: (   0.00, -10.00)
#   315°: (   7.07,  -7.07)
#   360°: (  10.00,   0.00)
#
# (3,4) 旋转0° -> (3.00, 4.00)
# (3,4) 旋转90° -> (-4.00, 3.00)
# (3,4) 旋转180° -> (-3.00, -4.00)
# (3,4) 旋转270° -> (4.00, -3.00)