Simple Trigonometric Equations | 简单三角方程

📚 Simple Trigonometric Equations | 简单三角方程

Welcome to this Edexcel A-level Mathematics revision guide on simple trigonometric equations. We will cover how to solve equations such as sin θ = 0.5, cos 2θ = √3/2 and tan θ = 1 within a given interval, using CAST diagrams, exact values and angle transformations.

欢迎阅读这篇 Edexcel A-level 数学复习指南，主题是简单三角方程。我们将学习如何在指定区间内求解 sin θ = 0.5、cos 2θ = √3/2 和 tan θ = 1 等方程，所用工具包括 CAST 图、特殊角精确值和角度变换。

1. What Are Simple Trigonometric Equations? | 什么是简单三角方程？

A trigonometric equation contains at least one trigonometric function of an unknown angle, such as sin θ, cos θ or tan θ. In this topic, we focus on equations where one of these functions is equal to a constant, for example sin θ = 0.5, cos θ = -√3/2 or tan θ = 1.

三角方程是含有未知角的正弦、余弦或正切等三角函数的方程。本主题重点讨论其中一个函数等于常数的情形，例如 sin θ = 0.5、cos θ = -√3/2 或 tan θ = 1。

Unlike basic algebraic equations, trigonometric equations usually have more than one solution in a full cycle. This is because the sine, cosine and tangent functions repeat their values as the angle increases. Edexcel questions therefore ask for all solutions in a stated interval, such as 0° ≤ θ < 360° or 0 ≤ θ < 2π.

与基本代数方程不同，三角方程在一个完整周期内通常有多个解。这是因为正弦、余弦和正切函数会随着角度增加而重复取值。因此 Edexcel 考题通常要求在指定区间内求出所有解

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