📚 Example 6.2.1: Solving Quadratic Trigonometric Equations | 例 6.2.1：解二次型三角方程
This worked example is a typical AQA AS-Level Pure Mathematics question on trigonometric equations. It combines quadratic factorisation with the exact values of sine and the use of a given interval.
这道例题是 AQA AS 阶段纯数学中典型的三角方程题。它把二次因式分解与正弦的精确值以及指定区间结合起来考查。
1. Why This Example Matters | 为什么这道例题很重要
ons such as sin x = k, cos x = k and tan x = k within a stated interval, often in degrees.
在 AQA 考试大纲中，三角方程属于纯数学部分。你需要会解 sin x = k、cos x = k 和 tan x = k 这类方程，并且经常要求在指定角度区间内求解。
This example goes one step further by hiding the trigonometric equation inside a quadratic expression. Many students lose marks because they stop after solving for sin x and forget to find all values of x.
这道例题更进一步，把三角方程隐藏在二次表达式里。许多学生丢分是因为他们求出 sin x 后就停了，忘记继续求出所有 x 的值。
Understanding this method will also help you with harder equations involving cos x and tan x, including those set in radians.
理解这个方法还能帮助你解决涉及 cos x 和 tan x 的更复杂方程，包括弧度制下的
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