How do you graph r=cos(θn) for n=3, 5, 7, 9 and how do you predict the shap of the graph for r=cos(θ11)?

2 Answers
Aug 12, 2018

See the method and the idiosyncratic graph of r=cos(θ11)
I would edit my answer myself, if necessary, before closure, on 8/15.

Explanation:

Why even n is not included? In my earlier answers, I had discussed all, including r=cos((mn)θ).

It appears that there is no identity ( even pseudonym ) for the

source of this question. In this medium, I have had disseminated,

within the limit of what I really know, without fear or favor. So, for

just one more day, I will do it..

Here, I had already solved such problems, that were never solved

before, through Cartesian conversions that care for suppressing

pixels in the graph, for invalid non-negative r=x2+y2

A reference:. .
https://socratic.org/questions/how-do-you-graph-r-cos-theta-n-for-n-2-4-6-and-8-and-how-do-you-predict-the-shap?source=search

I would repeat the method for r=cos(θ11).

#x/r = cos theta = cos 11(theta/11),

( and upon expanding in the Euler's mode, and using

a=θ11,c=cosaands=sina

x=c1255(c10s2c3s9)+330(c8s4c4s7)

462c6s6

Use c = r and s = sqrt ( 1-c^2 ).

The function for Socratic graphics utility is immediate.
graph{x - ((x^2+y^2)^6-55((x^2+y^2)^5(1-x^2-y^2)-(x^2+y^2)^1.5(1-(x^2+y^2))^4.5)+ 330((x^2+y^2)^4(1-x^2-y^2)^2-(x^2+y^2)^2.5(1-(x^2+y^2))^3.5)-462(x^2+y^2)^3(1-(x^2+y^2))^3)=0[-2. 2 -1 1 ] }

Aug 12, 2018

I am continuing my answer, for some remarks. I dislike editing my answer now, despite my statement that I would do it myself.. Anyone liking that can do so, after Aug 15.