Analyze the Graph of the Given Polar Curve $$r = 3 \cos 3 \theta - \sin 3 \theta$$

question 180

Essay

Analyze the graph of the given polar curve. Include the following information: 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 that the graph has. Give the equations of any
asymptotes or state that the graph has no asymptotes.
- $$r = 3 \cos 3 \theta - \sin 3 \theta$$

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Definitions:

Area

is a measure of the extent of a two-dimensional surface or shape, expressed in square units.

Biosphere

The global ecological system integrating all living beings and their relationships, including their interaction with the elements of the lithosphere, hydrosphere, and atmosphere.

Inhabited

Being lived in or occupied by people, animals, or other organisms.

Organisms

Individual living entities that can carry out life processes independently.