三角函数六大模型图解揭秘
引言
三角函数是数学中重要的组成部分，尤其在解决几何问题和物理现象时具有广泛应用。以下是三角函数的六大模型及其图解，帮助读者更好地理解这些函数。
一、正弦函数（y = sin(x)）
图解：
- 图像特征：正弦函数图像是一个周期性的波形，其周期为 (2\pi)。
- 对称性：正弦函数是奇函数，关于原点对称。
- 值域：([-1, 1])。
示例图解：
y = sin(x) | 1| __ | / | / | / | / | / |/ ———————– x
### 二、余弦函数（y = cos(x)）
#### 图解：
- **图像特征**：余弦函数图像与正弦函数图像相似，但相位差为 \(\pi/2\)。
- **对称性**：余弦函数是偶函数，关于y轴对称。
- **值域**：\([-1, 1]\)。
#### 示例图解：
```markdown
y = cos(x) | 1| __ | / | / | / | / |/ ———————– x
### 三、正切函数（y = tan(x)）
#### 图解：
- **图像特征**：正切函数图像具有垂直渐近线，周期为 \(\pi\)。
- **对称性**：正切函数是奇函数，关于原点对称。
- **值域**：全体实数。
#### 示例图解：
```markdown
y = tan(x) | |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |/ |