Answer: \(y\)-intercept \(=4\), maximum \((180^\circ,9)\), minimum \((-180^\circ,-1)\), endpoints \((-360^\circ,4)\) and \((360^\circ,4)\).

Start by taking the key information from the graph or diagram, such as intercepts, turning points, amplitudes, periods, or intersection points. Then use the relevant algebra to justify the result.

The graph is \(y=4+5\sin\frac{\theta}{2}\).

When \(\theta=0^\circ\), \(y=4+5\sin0^\circ=4\), so the \(y\)-intercept is \(4\).

When \(\theta=180^\circ\), \(\frac{\theta}{2}=90^\circ\), so \(y=4+5=9\). This is the maximum point.

When \(\theta=-180^\circ\), \(\frac{\theta}{2}=-90^\circ\), so \(y=4-5=-1\). This is the minimum point.

At \(\theta=-360^\circ\) and \(\theta=360^\circ\), \(\sin\frac{\theta}{2}=0\), so the graph has endpoints \((-360^\circ,4)\) and \((360^\circ,4)\).

This gives the required answer: \(y\)-intercept \(=4\), maximum \((180^\circ,9)\), minimum \((-180^\circ,-1)\), endpoints \((-360^\circ,4)\) and \((360^\circ,4)\).