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 ...

To sketch the graph of a polar equation a good first step is to sketch the graph in the Cartesian coordinate system. This will give a way to visualize how r changes with θ. The information about how r ...

The Monthly publishes articles, as well as notes and other features, about mathematics and the profession. Its readers span a broad spectrum of mathematical interests, and include professional ...