How do you graph #r=3sin7theta#?

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Answer 1 · 2018-07-08T12:06:44

See graph and the explanation.

Perform conversion of #r = 3 sin 7theta# to Cartesian frame, using

#sin 7theta = 7 cos^6theta sin theta - 35 (cos^4theta sin^3theta #

# + cos^2theta sin^5theta - sin^7theta)#

(from #e^(i 7theta) = (e^(i theta))^7# (Glory to De Moivre ))

and the conversion formula

# ( x, y ) = r ( cos theta, sin theta), r = sqrt( x^2 + y^2 ) >= 0#

and get

#( x^2 + y^2 )^4 =3 (7 x^6 y - 35 x^4 y^3 + 21 x^2 y^5 - y^7)#.

In the Cartesian frame, there is no glow of pixels, for invalid

negative r

Now the super graph appears here.

graph{( x^2 + y^2 )^4 -3 (7 x^6 y - 35 x^4 y^3 +21 x^2 y^5 - y^7)=0[-7 7 -3.5 3.5]}