📚 Secant, Cosecant and Cotangent | 正割、余割与余切
In A-Level Edexcel Mathematics, secant (sec), cosecant (cosec) and cotangent (cot) are the reciprocal trigonometric functions. They are built directly from cosine, sine and tangent, and they appear throughout identities, equations, graph sketching and calculus problems. Mastering their definitions, exact values and key identities is essential for high marks.
在 A-Level Edexcel 数学中，正割（sec）、余割（cosec）和余切（cot）是三个倒数三角函数。它们由余弦、正弦和正切直接构造而来，广泛出现在恒等式、方程、图像和微积分题目中。熟练掌握它们的定义、精确值和核心恒等式是取得高分的关键。
1. Definitions of the Reciprocal Ratios | 三个倒数比的定义
For any angle θ where the relevant denominator is non-zero, the three functions are defined as follows:
对于任意使得分母不为零的角 θ，三个函数的定义如下：
| Function | Definition | Equivalent form | Undefined when |
|---|---|---|---|
| sec θ | 1 / cos θ | 1 / cos θ | cos θ = 0, i.e. θ = 90° + 180°n |
| cosec θ | 1 / sin θ | 1 / sin θ | sin θ = 0, i.e. θ = 180°n |
| cot θ | 1 / tan θ | cos θ / sin θ | sin θ = 0, i.e. θ = 180°n |
Note that sec θ is paired with cosine, cosec θ with sine, and cot θ with tangent or the quotient of cosine and sine. This pairing is often the first point to check in algebraic manipulation.
请注意，sec θ 与余弦配对，cosec θ 与正弦配对，cot θ 与正切配对，也可写成余弦除以正弦。这种配对关系通常是代数变形
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