Exercise. Determine if each graph is a reasonable graph of the given equation.
r = 1 + cos θ for 0≤ θ ≤ π
Check a couple of points. When θ = 0 we should have
r = 1 + cos0 = 2.
When θ = π we should have
r = 1 + cosπ = 0.
These points are on the graph. However, for 0 ≤ θ ≤ π the value
r = 1 + cos θ
is positive. We should be seeing points in the first and second quadrants.
Since the graph we were given shows points in the third and fourth quadrants, it's the wrong graph.