First, notice that since cos *θ* is always between -1 and +1, the quantity *r *= 1 + cos *θ*
is always between 0 and 2. In particular, *r* will never be negative. We should find points in every quadrant. Find the value of *r* at some nice angles. This gives us some points to start from. Now we need to figure out what's going on in between these points. Remember that *r* is never negative. From *θ* = 0 to , the value of *r* will move from 2 to 1. From to θ = π, the value of *r* will move from 1 to 0. From θ = π to , the value of *r* will move from 0 to 1. From to θ = 2π, the value of *r* will move from 1 to 2. We end up with a heart shape that looks nothing like the graph *r* = cos *θ*. The moral of the story is that we typically use calculators when making anything but the simplest of graphs in polar coordinates.. |