IB CCEA Maths: Trigonometry – Key Exam Points | IB CCEA 数学：三角函数考点精讲

📚 IB CCEA Maths: Trigonometry – Key Exam Points | IB CCEA 数学：三角函数考点精讲

Trigonometry is a cornerstone of the IB CCEA Mathematics curriculum, encompassing radian measure, trigonometric graphs, identities, equation-solving, and calculus applications. Mastery of these topics is essential for success in both Pure and Applied components. This guide consolidates the key concepts, common pitfalls, and exam techniques you need for high-scoring answers.

三角函数是 IB CCEA 数学课程的核心支柱，涵盖弧度度量、三角函数图像、恒等式、方程求解以及微积分应用。牢固掌握这些内容对纯数与数学应用题都至关重要。本指南全面总结关键概念、常见易错点与应试技巧，助你在考试中脱颖而出。

1. Radian Measure and Degree Conversion | 弧度制与角度弧度转换

Radian measure is defined so that an angle subtended by an arc of length r on a circle of radius r is 1 radian. The full revolution of 360° equals 2π radians. Using radians is mandatory in calculus and simplifies many formulae.

弧度制度的定义为：在半径为 r 的圆上，长度为 r 的弧所对的圆心角是 1 弧度。一整圈 360° 等同于 2π 弧度。在微积分中必须使用弧度制，它也能简化许多公式。

π rad = 180°

To convert from degrees to radians, multiply by π/180. Conversely, multiply radians by 180/π to obtain degrees. Always express radian measures in exact form (e.g., π/3) unless decimal approximation is requested.

将角度转换为弧度，乘以 π/180；将弧度转换为角度，乘以 180/π。除非题目要求近似值，否则弧度应保留精确形式（如 π/3）。

Arc length: s = rθ and sector area: A = ½ r²θ, where θ is in radians. These appear frequently in geometric problems and area of segment calculations.

弧长公式 s = rθ，扇形面积公式 A = ½ r²θ，其中 θ 以弧度为单位。这些公式常见于几何问题与弓形面积计算。

2. The Unit Circle and Trigonometric Ratios | 单位圆与三角函数比

The unit circle (radius 1, centre at origin) defines sine and cosine for any angle θ measured from the positive x‑axis. Coordinates of the point on the circle are (cos θ, sin θ). Consequently, tan θ = sin θ / cos θ = y / x (cos θ ≠ 0).

单位圆（半径为 1，圆心在原点）为任意从正 x 轴量起的角度 θ 定义了正弦和余弦。圆周上点的坐标为 (cos θ, sin θ)。因此，tan θ = sin θ / cos θ = y / x（cos θ ≠ 0）。

Exact values for special angles must be instant: 0°, 30°, 45°, 60°, 90° and their radian equivalents. The table below summarises them; learn these off by heart.

特殊角的精确值必须烂熟于心：0°、30°、45°、60°、90° 及其弧度值。下表汇总了这些值，务必熟记。