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CAIE A-Level Mathematics 1.4.1 Radians

Practise finding angles in radians from diagrams, symmetry and trigonometry, including exact multiples of π and decimal answers.

Syllabus
2028–2030
Course
Mathematics 9709
Level
AS

Exam points

  • use symmetry, sine, cosine rule or right-triangle ratios to justify angles in radians
  • convert degree working into radians and state exact fractions of π where required

1.4.1—Radians question 1

[Maximum number: 1]
Figure for Question 1.4.1—Radians question 1 — CAIE A-Level Mathematics AS

The diagram shows a motif formed by the major arc A B of a circle with radius r and centre O, and the minor arc⁡AOB\operatorname{arc} A O B of a circle, also with radius r but with centre C. The point C lies on the circle with centre O.

Given that angle ACB=kπA C B=k \pi radians, state the value of the fraction k.

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