Page 55 - Calculus for the Clueless

There are a few others, but these are the main ones. Let us graph a couple of these to show the technique.

Example 6—

Graph r = 4(1 - cos θ).

θ r

0 4-4=0

π/6 4 - 2(3) 1/2 = .6

π/4 4 - 2(2) 1/2 = 1.2

π/3 4 - 2 = 2

π/2 4 - 0 =4

2π/3 4 + 2 = 6

3π/4 4 + 2(2) 1/2 = 6.8

5π/6 4 + 2(3) 1/2 = 7.4

π 4+4=8

Note

We have symmetry with respect to the x-axis. So we need only values of θ between 0 and π to reflect the image
in the x-axis. Note the chart. If you study the patterns, you should be able to do much of the table by sight. Also,
1/2
1/2
you know the approximate value of 2 (1.4) and 3 (1.7).
Note

There is a short way to draw the previous graph (and other graphs) if you know what the graph is. Find the
intercepts 0, π/2, θ, 3π/2, and sketch the graph around them (which is exactly how I did the graph).

Example 7—