Express the polar equation \(r=\cos 2\theta\) in rectangular coordinates. Find the maximum height above the \(x\)-axis of the cardioid \(r=1+\cos \theta\text{.}\) Sketch the graph of the curve whose ...

Plotting a graph takes time. Often mathematicians just want to know the key features. These are: shape, location and some key points (such as where the graph crosses the axes or turning points).