Review question

# Can we find the value of $\sin 18^\circ$ as a surd? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6018

## Question

1. Show that $\theta=18^\circ$ satisfies the equation $\cos 3\theta=\sin 2\theta$. By expressing $\cos 3\theta$ and $\sin 2\theta$ in terms of trigonometrical functions of $\theta$, show that $\sin 18^\circ$ is a root of the equation $4x^2+2x-1=0,$ and hence find its value as a surd.

2. Find all solutions between $0^\circ$ and $360^\circ$ of the equation $4\tan 2x=\cot x.$