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How do you graph #r=4cos7theta#?

Answer 1

Elijah Alexander

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]}

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.