Graphing with polar coordinates Problem

[Modest Learner]

Homework Statement

Draw the graph of r = 1/2 + cos(theta)

Homework Equations

The equation is itself given in the question. It is a Limacon.

The Attempt at a Solution

Step-1 ---> Max. value of r is 1/2 + 1 = 3/2 [ at cos (0) ]
Min. value of r is 1/2 - 1 = -1/2 [ at cos (Pi) ]

Step-2 ---> Symmetry The curve is symmetrical about x-axis.

Step-3 ---> I calculated all the values of "r" from 0 to 180 degrees. These are 1.5, 1.336, 1.207, 1, 0.5, 0, -0.207, -0.336, -0.5. These are in standard form like 0, 30, 45... and so on.

Step-4 ---> Now I draw the graph. Till 90 degrees its all right; but at 120 degrees the problem comes. How can I draw show 0 as well as 120 degrees? How can I show (-0.5, 180 degrees) ?

 

[ArcanaNoir]

Pretend you are drawing 0.5 at 180 degree, but since the radius is negative, flip it back to positive 0.5 at 0 degrees.

 

[Modest Learner]

Okay, thanks a lot.