Edexcel A-Level Maths: Trigonometric Ratios and Equations | Edexcel A-Level 数学：三角比与三角方程

📚 Edexcel A-Level Maths: Trigonometric Ratios and Equations | Edexcel A-Level 数学：三角比与三角方程

Trigonometric ratios and equations are central to the Edexcel A-Level Mathematics specification. They appear in pure mathematics questions on triangles, graphs, identities and real-world modelling. A secure command of sine, cosine, tangent, exact values and equation-solving is essential for high marks.

三角比与三角方程是 Edexcel A-Level 数学大纲的核心内容。它们在纯数学的三角形、图像、恒等式和实际问题建模中反复出现。熟练掌握正弦、余弦、正切、特殊角精确值以及解三角方程是取得高分的关键。

1. Sine Rule | 正弦定理

For any triangle ABC with sides a opposite A, b opposite B and c opposite C, the sine rule states:

a / sin A = b / sin B = c / sin C

Use the sine rule when you know two angles and one side (AAS or ASA) or two sides and a non-included angle (SSA). In the SSA case, check for the ambiguous case: two possible triangles may exist.

对于任意三角形 ABC，边 a 对角 A，边 b 对角 B，边 c 对角 C，正弦定理为上述公式。

当已知两角一边（AAS 或 ASA）或两边及一个非夹角（SSA）时使用正弦定理。在 SSA 情形中要检查“不确定情形”：可能存在两个符合条件的三角形。

Example: given A = 30°, B = 80° and a =

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