How do you graph r2=−cosθ?

1 Answer
A. S. Adikesavan
Sep 1, 2016

See the combined graph that includes an elongated circle depicting this equation, and read the related important note on r2.

Explanation:

Here, I introduce the meaningful interpretations for the presence of

kr,rmandmθ, in polar equations. This is important to

understand equations that have some family characteristics.

Examples:

r=−cosθ,r2=−cosθ,r=−cos2θ,

r2=−cos2θ, and so on.

On par with scaling x and y in Cartesian frame,

power scaling of r, r2 increases/reduces lengths and just

multiplication of θ by scalars, like 2θ,θ2 produce

slower/faster rotations, about the pole.

See the combined graph for r=−cosθ,r2=−cosθ,

r=−cos2θandr2=−cos2θ.

It would be interesting to know, which is which.

The graph of r2=−cosθ is the elongated circle. Compared

to the circle r=−cosθ, the point (1√2,3π4) moves to

(1√√2,3π4), in that direction. See the graph, for this r-

scaling effect.

graph{(x^2+y^2+x)((x^2+y^2)^1.5+x)((x^2+y^2)^1.5+x^2-y^2)((x^2+y^2)^2+x^2-y^2)(y+x)((x+0.6)^2+(y-.6)^2 - .0015)((x+0.5)^2+(y-0.5)^2-0.001)=0[-2 2 -1.1 1.1]}

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