What is the shape of the graph r2=−cosθ?

2 Answers
Cesareo R.
Aug 31, 2016

Correcting an error.

Explanation:

This graph is for π2≤θ≤3π2

r2=−cosθ

with

r=±√−cosθ

See the attached plot.

enter image source here

A. S. Adikesavan
Aug 31, 2016

See explanation for the loop.

Explanation:

As r=f(cosθ)=f(cos(−θ)), the shape is symmetrical about

the initial line

r2=−cosθ≥0,θ∈(12π,32π), wherein cosθ≤0.

I strictly stick to the definition of (length) r as non-negative.

The Table for plotting the graph is

(r,θ):

(0,π2)(1√2,23π)(1√√2,34π)⎛⎝√√32,56π⎞⎠(1,π)

Symmetry about the axis θ=π is used to draw the other

half of the loop.

Note that I have considered only one loop from

r=√−cosθ≥0

and did not consider the non-positive

r=−√−cosθ≤0,

for the opposite loop, for the same

θ∈(12π,32π).

My r is a single-valued function of θ.

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