Review question

# Can we solve these simultaneous trigonometric equations? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R7604

## Question

1. Given that $x=1+2\cos\theta$, prove that $x^3-3x^2+1= 2\cos 3\theta-1$.

Using this result, or otherwise, find each of the three roots of the equation $x^3-3x^2+1=0$, giving your answers correct to 3 places of decimals.

2. The values of $x$ and $y$ satisfy the equations \begin{align*} 3\cos^2 x+ 2\cos^2 y&=4,\\ 3\sin 2x-2\sin 2y&=0. \end{align*}

Find the values of $\cos 2x$ and $\cos 2y$.

Hence find, to the nearest degree, four pairs of corresponding values of $x$ and $y$, all values lying between $0^\circ$ and $360^\circ$.