How do you graph $r=4cos7theta$ ?

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Answer 1 · 2017-01-11T11:42:03

See the 7-petal rose and explanation.

$cos 7theta$ is periodic, with period $(2pi)/7$ .

$r = 4 cos 7theta >= 0 and <=4$

So, the complete rotation through $2pi$ would create

7 petals @ 1 petal/period.

All these petals are contained in a square of side

2 (size of a petal) = 2 (4) = 8 units.

The cartesian form for $r = 4 cos 7theta$ is

$(x^2+y^2)^2sqrt(x^2+y^2)=4(x^7-21x^5y^2+35x^3y^4-7xy^6)$

and this was used, for making the Socratic graph.

graph{(x^2+y^2)^4-4(x^7-21x^5y^2+35x^3y^4-7xy^6)=0 [-15, 15, -7.5, 7.5]}

How do you graph r=4cos7thetar=4cos7theta?