This question has 2 part(s).

On the same set of axes, sketch the graphs of $y=tan\frac{1}{2} \theta$ and $y=tan( \theta -30^{\circ})$ in the interval $-360^{\circ}\leq \theta \leq360^{\circ}$. Label the coordinates of points of intersection with the coordinate axes.

A function $f(x)=cospx$,$0^{\circ}\leqx\leq360^{\circ}$, first crosses the $x$-axis at $18^{\circ}$.

(i) Determine the value of $p$ and sketch the graph of $y=f(x)$.

(ii) State the period of $f(x)$.

Within the interval $-360^{\circ}\leq \theta \leq360^{\circ}$, determine the coordinates of the two points where $tan\frac{1}{2} \theta =tan( \theta -30^{\circ})$. Give your answer in surd form.