How do you graph r=4cos7thetar=4cos7θ?

1 Answer
A. S. Adikesavan
Jan 11, 2017

See the 7-petal rose and explanation.

Explanation:

cos 7thetacos7θ is periodic, with period (2pi)/72π7.

r = 4 cos 7theta >= 0 and <=4r=4cos7θ≥0and≤4

So, the complete rotation through 2pi2π 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 7thetar=4cos7θ is

(x^2+y^2)^2sqrt(x^2+y^2)=4(x^7-21x^5y^2+35x^3y^4-7xy^6)(x2+y2)2√x2+y2=4(x7−21x5y2+35x3y4−7xy6)

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]}

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