We need to sketch `r = 2.5`

In this example, we cannot see "θ" in the function we are given. This means the radius, r is constant, no matter what value angle θ takes.

Here's the graph:

30°60°90°120°150°180°210°240°270°300°330°0123Open image in a new page

Graph of r = 2.5, a limacon.

What is the Equivalent in Rectangular Coordinates?

We convert the function given in this question to rectangular coordinates to see how much simpler it is when written in polar coordinates.

To convert `r = 2.5` into rectangular coordinates, we use

r2 = x2 + y2

In this example, `r = 2.5`, so `r^2= 6.25`.

So this gives us: x2 + y2 = 6.25

Not surprisingly, this is the similar to the equation for a circle we obtained in The Circle section earlier.

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