📚 IGCSE Maths: Trigonometry and Pythagoras Theorem | IGCSE 数学：三角函数与毕达哥拉斯定理
Trigonometry and Pythagoras' theorem are core topics in the IGCSE Mathematics syllabus. They appear in both calculator and non-calculator papers, often combined with area, bearings and real-life context problems.
三角函数与毕达哥拉斯定理是 IGCSE 数学大纲中的核心内容。它们常出现在可用计算器和不可用计算器的试卷中，并且经常与面积、方位角和实际情境问题结合考查。
1. Pythagoras' Theorem | 毕达哥拉斯定理
In any right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The hypotenuse is always the longest side and is opposite the right angle.
在任何直角三角形中，斜边的平方等于另外两条边的平方和。斜边总是最长边，并且位于直角的对面。
c² = a² + b²
d also works backwards: if you know the hypotenuse and one shorter side, subtract the squares to find the other side.
如果 a = 6 cm，b = 8 cm，则 c² = 6² + 8² = 36 + 64 = 100，所以 c = √100 = 10 cm。此方法也可以反向使用：如果已知斜边和一条直角边，用斜边平方减去已知直角边平方，再开方即可求出另一条直角边。
2. Trigonometric Ratios: Sine, Cosine and Tangent | 三角函数比：正弦、余弦与正切
adjacent / hypotenuse, and tan θ = opposite / adjacent. A common memory aid is SOHCAHTOA.
三个三角函数比将直角三角形中的角与其边长之比联系起来。它们定义为 sin θ = 对边 / 斜边，cos θ = 邻边 / 斜边，tan θ = 对边 / 邻边。常用的记忆口诀是 SOHCAHTOA。
sin θ = Opposite / Hypotenuse
cos θ = Adjacent / Hypotenuse
tan θ = Opposite / Adjacent
When labelling a triangle, the opposite side is directly across from the angle θ, the adjacent side is next to θ but not the hypotenuse, and the hypotenuse is always opposite the right angle.
在标记三角形时，对边是角 θ 正对着的边，邻边是与 θ 相邻但不是斜边的边，而斜边始终是直角对面的边。
3. Choosing the Right Ratio | 选择正确的三角函数
To decide which ratio to use, label the sides relative to the given angle: opposite, adjacent, and hypotenuse. Then ask which two sides are involved in the problem. If the hypotenuse is unknown or given, sine or cosine is usually needed; if both legs are involved, tangent is used.
要确定使用哪个三角函数比，先根据给定角标记各边：对边、邻边和斜边。然后判断题目中涉及的是哪两条边。如果涉及斜边，通常使用正弦或余弦；如果只涉及两条直角边，则使用正切。
θ = opposite / adjacent. If you know the hypotenuse and want the opposite side, use sine.
例如，如果已知一个角和邻边，要求对边，使用 tan θ = 对边 / 邻边。如果已知斜边并要求对边，则使用正弦。
4. Finding Missing Sides | 求未知边
gle where θ = 35° and the hypotenuse is 12 cm, the opposite side x satisfies sin 35° = x /
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