The question is asking us to create a polar plot of a function of angle, theta, which gives us r, the distance from the origin. Before starting we should get an idea of the range of r values we can expect. That will help us decide on a scale for our axes.
The function cos(theta) has a range [-1 ,+1] so the quantity in parentheses 1+cos(theta) has a range [0,2]. We then multiply that by 2a giving:
r=2a(1+cos(theta)) in [0,4a]
This is the ditance to the origin, which could be at any angle, so let's make our axes, x and y run from -4a to +4a just in case:
Next, it's useful to make a table of the value of our function. We know that theta in [0,360^o] and let's break it up into 25 points (we use 25 because that makes 24 steps between points which are angles of 15^o):
![enter image source here]()
Where we have also included a calculation of the Cartesian coordinates of each point where x=r*cos theta and y=r*sin theta. We now have a choice, we can plot the points using a protractor for the angle and a ruler for the radius, or just use the (x,y) coordinates. When you are done, you should have something that looks like this:
![enter image source here]()
