Question

How do you graph `r=3sin7theta`?

Answer 1

See graph and the explanation.

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]}