CAIE A-Level Mathematics AS 1.4.1 Radians Questions

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

Exam points

Determine exact radian angles from geometric relationships, symmetry or sector structure, expressing results as fractions or multiples of π.
Express a geometrically determined angle as a fraction k in kπ radians, using the diagram and established angle relationships.

[Maximum number: 1]

Figure for Question CAIE A-Level Mathematics AS 1.4.1 Radians Questions 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 $\operatorname{arc} A O B$ of a circle, also with radius r but with centre C. The point C lies on the circle with centre O.

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

$k=\frac{2}{3}$
Marking guidance:

Allow $\mathrm{ACB}=\frac{2 \pi}{3}$ .

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CAIE A-Level Mathematics AS 1.4.1 Radians Questions question 1