Trigonometry and Modelling

a.

By writing $\sin 3\theta\,$ as $sin⁡(2θ+θ)\sin(2\theta + \theta)$ , show that $sin⁡3θ=3sin⁡θ−4sin⁡3θ\sin 3\theta = 3\sin\theta - 4\sin^3\theta$

[2]

b.

Solve, for $\leq \theta \leq \pi$ , the equation,

3\sin\theta - 4\sin^3\theta = 0.5

Give your answers in terms of $π\pi$ .

[4]

a.

By writing $\sin 3\theta\,$ as $sin⁡(2θ+θ)\sin(2\theta + \theta)$ , show that $sin⁡3θ=3sin⁡θ−4sin⁡3θ\sin 3\theta = 3\sin\theta - 4\sin^3\theta$

[2]

b.

Solve, for $\leq \theta \leq \pi$ , the equation,

3\sin\theta - 4\sin^3\theta = 0.5

Give your answers in terms of $π\pi$ .

[4]

Trigonometry and Modelling Questions