Chapter Review 9: Trigonometric Ratios | 第9章复习：三角比

📚 Chapter Review 9: Trigonometric Ratios | 第9章复习：三角比

This chapter review covers the core ideas of trigonometric ratios for Edexcel A-Level Mathematics. You will revisit the definitions of sine, cosine and tangent, exact values for key angles, the unit circle, graphs, and strategies for solving simple trigonometric equations. Mastery of these basics is essential before moving on to trigonometric identities and equations in later chapters.

本章复习涵盖 Edexcel A-Level 数学中三角比的核心概念。你将重温正弦、余弦和正切的定义，关键角的精确值、单位圆、函数图像，以及解简单三角方程的策略。在进入后续章节的三角恒等式与方程之前，牢固掌握这些基础至关重要。

1. The Sine, Cosine and Tangent Ratios | 正弦、余弦和正切比

For a right-angled triangle, label the sides relative to an acute angle θ: the opposite side is across from θ, the adjacent side is next to θ (not the hypotenuse), and the hypotenuse is the longest side.

对于直角三角形，相对于锐角 θ 标记边：对边在 θ 的对面，邻边紧邻 θ（不是斜边），斜边是最长边。

The three basic trigonometric ratios are defined as follows, where opposite means the side opposite θ, adjacent means the side adjacent to θ, and hypotenuse is the longest side.

三个基本三角比定义如下，其中 opposite 表示 θ 的对边，adjacent 表示 θ 的邻边，hypotenuse 是最长边。

sin θ = opposite / hypotenuse, cos θ = adjacent / hypotenuse, tan θ = opposite / adjacent

Remember the abbreviation SOH CAH TOA: Sine is Opposite over Hypotenuse, Cosine is Adjacent over Hypotenuse, Tangent is Opposite over Adjacent.

记住缩写 SOH CAH TOA：正弦是对边除以斜边，余弦是邻边除以斜边，正切是对边除以邻边。

These ratios only apply to right-angled triangles. For non-right-angled triangles, you will need the sine rule or cosine rule, which are covered in later chapters.

这些比只适用于直角三角形。对于非直角三角形，你需要使用正弦定理或余弦定理，它们将在后续章节中学习。

2. Exact Values for Special Angles | 特殊角的精确值

You must know the exact values for 0°, 30°, 45°, 60° and 90° without a calculator. These arise from an equilateral triangle (for 30° and 60°) and an isosceles right triangle (for 45°).

你必须在不使用计算器的情况下知道 0°、

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