CAIE A-Level Mathematics AS 2.3.2 Trig Identities Questions

Practise choosing trig identities to simplify expressions, prove results and solve equations within stated angle intervals.

Exam points

use vector notation and operations
solve geometric problems with vectors
interpret vector relationships

[Maximum number: 3]

It is given that $\theta$ is an acute angle in degrees such that $\sin \theta=\frac{2}{3}$ .
Find the exact value of $\sin \left(\theta+60^{\circ}\right)$ .

State or imply that $\cos \theta=\frac{1}{3} \sqrt{5}$
or exact equivalent.

Substitute appropriate values into $\sin \theta \cos 60^{\circ}+\cos \theta \sin 60^{\circ}$
Obtain $\frac{1}{3}+\frac{1}{6} \sqrt{15}$
or exact equivalent.

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CAIE A-Level Mathematics AS 2.3.2 Trig Identities Questions question 1