Question

How do you graph `r=4cos7theta`?

Answer 1

See the 7-petal rose and explanation.

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]}