Edexcel A Level Pure Maths: Trigonometric Modelling with Rsin(θ ± α) | Edexcel A Level 数学：用 Rsin(θ ± α) 进行三角函数建模

📚 Edexcel A Level Pure Maths: Trigonometric Modelling with Rsin(θ ± α) | Edexcel A Level 数学：用 Rsin(θ ± α) 进行三角函数建模

In Edexcel A Level Mathematics, trigonometric modelling questions often ask you to rewrite expressions such as 3 sin θ + 4 cos θ in the form R sin(θ + α), then use that new form to solve equations, find maximum or minimum values and interpret real-world oscillations. This revision guide covers the compound-angle identities, double-angle formulae, the auxiliary-angle method, equation solving and exam technique.

在 Edexcel A Level 数学中，三角函数建模题通常要求你把 3 sin θ + 4 cos θ 这类表达式改写为 R sin(θ + α) 的形式，再利用该形式解方程、求最大值或最小值，并解释现实中的振动模型。本文复习复合角恒等式、倍角公式、辅助角方法、方程求解以及考试技巧。

1. Why Trigonometric Modelling Matters | 为什么三角函数建模重要

Edexcel Pure Mathematics Paper 2 regularly includes a modelling question involving compound angles or the auxiliary-angle method. These questions combine algebra, trigonometry and contextual interpretation, so they usually carry a high number of marks.

Edexcel 纯数学第二卷经常出现复合角或辅助角方法的建模题。这类题综合了代数、三角和情境解释，因此通常分值较高。

The key skill is not just remembering the formulae, but knowing how to transform a sum of sine and cosine terms into a single trigonometric function whose amplitude, period and phase shift can be read directly.

关键技能不仅在于记忆公式，更在于知道如何将正弦项与余弦项的和转化为一个单一三角函数，并直接读出其振幅、周期和相位移动。

This is especially useful in modelling because maximum and minimum values can be found without differentiation, and equations can be solved more easily after the rewrite.

这在建模中特别有用，因为无需微分即可求出最大值和最小值，而且改写后方程也更容易求解。

2. Compound-Angle Formulae at a Glance | 复合角公式速览

The compound-angle formulae are the foundation of trigonometric modelling. They are used to expand expressions such as R sin(θ ± α) and R cos(θ ± α).

复合角公式是三角函数建模的基础，用于展开 R sin(θ ± α) 和 R cos(θ ± α) 等表达式。

sin(A ± B) = sin A cos B ± cos A sin B

cos(A ± B) = cos A cos B ∓ sin A sin B

The tangent compound-angle formula is also useful when simplifying rational trigonometric expressions or solving equations involving tan(A ± B).

正切复合角公式在化简有理三角式或解含 tan(A ± B) 的方程时也很有用。

tan(A ± B) = (tan A ± tan B) / (1 ∓ tan A tan B)

Make sure you can reverse these expansions accurately. When expanding

Published by TutorHao | A-Level Mathematics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）