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:
Graph of r = 2.5, a limacon.
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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