Question

Analyze the graph of the given polar curve. If possible, describe the shape of the graph (circle, rose curve, limacon, etc), and state the domain, range, and maximum r-value of the graph. State whether the graph is continuous and whether it is bounded. Describe any symmetry the graph has. Give the equations of any asymptotes or state that the graph has no asymptotes. r = 3 - 3cos

Answer 1

Step-by-step explanation:

Given the polar curve

R= 3-3cosϴ (please have a look at the attached photo)

We have some properties of the function are:

• The domain are real numbers <=> ϴ ∈ R
• The shape of the curve is a rose curve
• The range is approximately from -3.9 to 3.9  <=> -3.9 ≤R ≤3.9

=> The maximum value : 3.9

• The graph is symmetrical about the x axis
• The graph is continuous and it is bounded above and below
• The graph has no asymptotes

Hope it will find you well.