Trigonometry and Modelling

a.

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

[2]

b.

Solve, for $\leq \phi \leq 180$ , the equation,

12\cos^3 \phi - 9\cos \phi = 1.5

Give your answers to 1 decimal place where necessary.

[4]

a.

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

[2]

b.

Solve, for $\leq \phi \leq 180$ , the equation,

12\cos^3 \phi - 9\cos \phi = 1.5

Give your answers to 1 decimal place where necessary.

[4]

Trigonometry and Modelling Questions