Edexcel Maths: Trigonometry – Essential Revision Guide | Edexcel 数学：三角函数 核心考点精讲

📚 Edexcel Maths: Trigonometry – Essential Revision Guide | Edexcel 数学：三角函数 核心考点精讲

Trigonometry is a cornerstone of Edexcel Mathematics, weaving through Pure, Mechanics, and Statistics. This comprehensive guide distils the essential concepts – from basic right‑triangle ratios to advanced compound‑angle identities – tailored for IGCSE and A‑Level learners. Mastery of these topics will sharpen your problem‑solving skills for equations, graphs, and real‑world applications.

三角函数是 Edexcel 数学的基石，贯穿纯数、力学和统计。这本综合指南浓缩了从基本直角三角形比到高级复合角恒等式的核心概念，为 IGCSE 和 A‑Level 学生量身定制。掌握这些主题将提升你在方程、图像和实际应用中的解题能力。

1. Trigonometric Ratios in Right Triangles | 直角三角形中的三角比

The three primary trigonometric ratios are sine (sin), cosine (cos), and tangent (tan).

三个主要的三角比是正弦 (sin)、余弦 (cos) 和正切 (tan)。

In a right‑angled triangle with an acute angle θ, sin θ = opposite / hypotenuse, cos θ = adjacent / hypotenuse, tan θ = opposite / adjacent.

在含有锐角 θ 的直角三角形中，sin θ = 对边 / 斜边，cos θ = 邻边 / 斜边，tan θ = 对边 / 邻边。

These relationships are often memorised with the acronym SOH CAH TOA.

这些关系通常用记忆口诀 SOH CAH TOA 来记住。

On the unit circle, the coordinates (cos θ, sin θ) define the cosine and sine of the angle measured from the positive x‑axis, extending the definitions to any real angle.

在单位圆上，坐标 (cos θ, sin θ) 定义了从正 x 轴起测得的角 θ 的余弦和正弦，将定义扩展到任意实角。

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

Exact trigonometric values for 0°, 30°, 45°, 60°, and 90° must be committed to memory – they form the basis for many exam questions without calculators.

必须牢记 0°、30°、45°、60° 和 90° 的精确三角函数值——它们是许多无计算器考题的基础。