Trigonometry and Modelling

a.

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

[2]

b.

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

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

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

[4]

a.

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

[2]

b.

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

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

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

[4]

Trigonometry and Modelling Questions