Mastering Trigonometry for IGCSE Mathematics | 掌握 IGCSE 数学三角学

📚 Mastering Trigonometry for IGCSE Mathematics | 掌握 IGCSE 数学三角学

Trigonometry is a cornerstone of the IGCSE Mathematics syllabus, appearing in both Core and Extended papers. It explores the relationships between the sides and angles of triangles, enabling us to solve practical problems in surveying, navigation, and engineering. This article will guide you through the essential trigonometric concepts and techniques required for exam success.

三角学是 IGCSE 数学教学大纲的基石，在核心（Core）和拓展（Extended）试卷中都会出现。它研究三角形各边与角之间的关系，使我们能够解决测量、航海和工程中的实际问题。本文将引导你掌握考试所需的核心三角概念与解题技巧。

1. What is Trigonometry? | 什么是三角学？

The word “trigonometry” comes from Greek words “trigonon” (triangle) and “metron” (measure). It is the branch of mathematics that studies the relationship between angles and sides of triangles. In IGCSE Mathematics, you first learn about the three basic trigonometric ratios in right-angled triangles, then extend this knowledge to solve problems involving any triangle using the sine rule and cosine rule.

“三角学”一词源自希腊语 trigonon（三角形）和 metron（测量）。它是研究三角形角和边之间关系的数学分支。在 IGCSE 数学中，你首先学习直角三角形中的三个基本三角比值，然后通过正弦定理和余弦定理，将这些知识扩展到任意三角形的求解。

Trigonometry is not just about calculating angles; it is widely applied in real life. Architects use it to design roof slopes, pilots use it for navigation, and physicists use it to analyse waves. A strong grasp of trigonometry will also be essential if you continue to A-Level Mathematics or Further Mathematics.

三角学不仅是计算角度那么简单，它在日常生活中应用广泛。建筑师用它来设计屋顶坡度，飞行员用它来导航，物理学家用它来分析波动。如果你后续学习 A-Level 数学或进阶数学，扎实掌握三角学同样至关重要。

2. Right-Angled Triangle Ratios (SOH CAH TOA) | 直角三角形比值

In a right-angled triangle, the three main trigonometric ratios are defined using the sides relative to one of the acute angles, θ. The hypotenuse is the longest side (opposite the right angle), the opposite side is the side opposite to θ, and the adjacent side is the side next to θ (but not the hypotenuse).

在直角三角形中，三个主要三角比值由相对于一个锐角 θ 的边来定义。斜边（hypotenuse）是最长边（直角所对）；对边（opposite）是与 θ 相对的边；邻边（adjacent）是组成 θ 角的另一条非斜边的边。

The three ratios are memorised using the mnemonic SOH CAH TOA:

这三个比值可以通过口诀 SOH CAH TOA 来记忆：

• sin θ = Opposite / Hypotenuse

• cos θ = Adjacent / Hypotenuse

• tan θ = Opposite / Adjacent

sin θ = O/H, cos θ = A/H, tan θ = O/A

For example, if we want to find a missing side, we choose the ratio that includes the given side and the missing side. If the angle is 30° and the hypotenuse is 10 cm, then sin 30° = opposite / 10, so opposite = 10 × sin 30° = 10 × 0.5 = 5 cm.

例如，若要求未知边长，我们选择包含已知边和未知边的比值。若角为 30°、斜边为 10 cm，则 sin 30° = 对边 / 10，即对边 =

Published by TutorHao | IGCSE Mathematics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）