IB & CIE Maths: Trigonometry – Key Concepts & Exam Tips | IB & CIE 数学：三角函数考点精讲

📚 IB & CIE Maths: Trigonometry – Key Concepts & Exam Tips | IB & CIE 数学：三角函数考点精讲

Trigonometry is a cornerstone of both IB and CIE mathematics syllabi. From solving right triangles with basic sine, cosine, and tangent ratios to manipulating complex identities and analysing periodic functions, a firm grasp of trigonometry is vital. This article consolidates key concepts, formulas, and exam-focused strategies to help you excel in your assessments.

三角学是IB和CIE数学教学大纲的基石。从使用基本正弦、余弦和正切比解直角三角形，到操作复杂的恒等式和分析周期函数，牢固掌握三角函数至关重要。本文将整合关键概念、公式和应试策略，助你在考试中脱颖而出。

1. Radian Measure & Angle Conversions | 弧度制与角度转换

Radian measure provides a natural way of describing angles based on the radius of a circle. One radian is defined as the angle subtended at the centre of a circle by an arc equal in length to the radius. The conversion linking degrees and radians is 180° = π rad. To convert degrees to radians, multiply by π/180. Conversely, multiply radians by 180/π to obtain degrees. Mastering radian mode is essential for calculus applications in trigonometric functions.

弧度制提供了一种基于圆半径来描述角度的自然方式。1弧度定义为弧长等于半径的圆心角。度与弧度的换算关系为180° = π弧度。将度数转换为弧度，乘以π/180。反之，将弧度乘以180/π可得到度数。掌握弧度模式对于三角函数中的微积分应用至关重要。

Common angle conversions include 30° = π/6, 45° = π/4, 60° = π/3, and 90° = π/2. Being fluent in these equivalents saves time in exams.

常见角度转换包括30° = π/6，45° = π/4，60° = π/3，90° = π/2。熟记这些等价关系能在考试中节省时间。

2. Trigonometric Ratios & the Unit Circle | 三角比与单位圆

The unit circle, centred at (0,0) with radius 1, defines trigonometric functions for any angle. For a point P on the circle corresponding to angle θ, the coordinates are (cos θ, sin θ). The tangent function is

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