Solving Trigonometric Equations | 三角函数方程求解

📚 Solving Trigonometric Equations | 三角函数方程求解

Trigonometric equations are a central part of the Edexcel A-Level Pure Mathematics specification. They require you to combine algebraic manipulation with the periodic nature of sine, cosine and tangent.

三角函数方程是 Edexcel A-Level 纯数学大纲的核心内容。这类题目要求你把代数变形与正弦、余弦和正切的周期性结合起来。

This guide explains the essential methods, identities and exam techniques needed to solve such equations accurately and efficiently, with fully worked examples.

本指南将讲解求解这类方程所必需的基本方法、恒等式和考试技巧，并配有完整例题。

1. Understanding the Problem | 理解题目要求

Before solving, read the question carefully. Edexcel questions usually give an equation and an interval, such as 0° ≤ θ ≤ 360° or 0 ≤ θ < 2π. You must find all solutions inside that interval.

解题前要仔细读题。Edexcel 题目通常会给出一个方程和一个区间，例如 0° ≤ θ ≤ 360° 或 0 ≤ θ < 2π。你必须找出该区间内的所有解。

Check whether exact values are required or whether decimal places are permitted. Many equations are designed to produce special angles such as 30°, 45°, 60° and their radian equivalents.

检查题目要求精确值还是允许小数。许多方程被设计成能得到特殊角，例如 30°、45°、60° 及其弧度等价形式。

You also need to remember that sine and cosine repeat every 360° or 2π

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