Trigonometry and Modelling

a.

Show that

\sin 3x \equiv 3 \sin x - 4 \sin^3 x

[4]

b.

Hence, solve, for $\leq \theta < \pi$ ,

\sin^3 \theta - 6 \sin \theta + k = 0

where $k\,$ is a constant such that $0 < k < 2$ .

Give your answers in terms of $k$ .

[5]

a.

Show that

\sin 3x \equiv 3 \sin x - 4 \sin^3 x

[4]

b.

Hence, solve, for $\leq \theta < \pi$ ,

\sin^3 \theta - 6 \sin \theta + k = 0

where $k\,$ is a constant such that $0 < k < 2$ .

Give your answers in terms of $k$ .

[5]

Trigonometry and Modelling Questions