Solve the multiple–angle sine equation .

MATHEMATICS · Multi-part · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Solve the multiple–angle sine equation

\sin 3x = \dfrac{1}{2}

. (i) Obtain the general solution for

3x

that satisfies

\sin 3x = \dfrac{1}{2}

. (ii) Hence, derive the general solution for

x

. (iii) List all solutions of

x

that lie in the interval

[0,\,2\pi)