Mastering Trigonometric Differentiation for Edexcel A-Level Pure Maths | 掌握Edexcel A-Level纯数学三角函数求导

📚 Mastering Trigonometric Differentiation for Edexcel A-Level Pure Maths | 掌握Edexcel A-Level纯数学三角函数求导

Trigonometric differentiation appears throughout the Edexcel A-Level Pure Mathematics specification, especially in Papers 1 and 2. You must be able to differentiate sin x, cos x and tan x confidently, then combine these results with the chain, product and quotient rules. This article explains the key formulas, common exam traps and worked examples you can use to improve your marks.

三角函数求导贯穿 Edexcel A-Level 纯数学大纲，尤其是 Paper 1 和 Paper 2。你必须能够熟练求出 sin x、cos x 和 tan x 的导数，并将这些结果与链式法则、乘法法则和除法法则结合。本文讲解关键公式、常见考试陷阱以及可以帮助你提高分数的例题。

1. Why Trigonometric Differentiation Matters | 为什么三角函数求导重要

In the Edexcel specification, differentiation of trigonometric functions is a core Pure Mathematics skill. It appears in questions on stationary points, tangents, normals, rates of change and integration, so any weakness here can affect many areas of the exam.

在 Edexcel 大纲中，三角函数求导是纯数学的核心技能。它出现在驻点、切线、法线、变化率和积分等题型中，因此这一部分的薄弱会影响到考试的许多方面。

Most exam questions are not simply ‘differentiate sin x’. They involve composite arguments, products or quotients, so you must understand the rules rather than memorise isolated results.

大多数考试题并不是简单地要求“对 sin x 求导”。它们涉及复合角、乘积或商，因此你必须理解法则，而不是孤立地背诵结果。

2. Standard Derivatives of sin x and cos x | sin x 与 cos x 的基本导数

The two fundamental results are:

两个基本结果是：

d/dx (sin x) = cos x

d/dx (cos x) = -sin x

Notice the negative sign in the derivative of cos x. This is one of the most common places to lose marks, so write it down before you start any problem involving cos x.

注意 cos x 导数中的负号。这是最常见的失分点之一，因此在开始任何涉及 cos x 的问题之前，请先写下这个负号。

These formulas are only valid when x is measured in radians. In A-Level calculus, always work in radians unless a question explicitly gives an angle in degrees and asks you to convert it first.

这些公式仅在 x 以弧度为单位时成立。在 A-Level 微积分中，

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