How do you graph #r=4cos4theta#?

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Answer 1 · 2017-01-25T04:43:38

See the 4-petal rose, in the Socratic graph. I have used the Cartesian equation, instead.

The period for the graph is #(2pi)/4=pi/2#.

The size of each petal, in this 4-petal rose, is 4.

As #r = sqrt(x^2+y^2)=4 cos 4theta>=0, 4theta in Q_1 or Q_4#,

and so,

the span of #theta#, for 1-period-petal, is

span of #(Q_1 +Q_4)#/4 = #pi/4#= 1/2(period).

In the other half of a period #pi/2, r < 0#, and it is vacant.

Overall, for one round #theta in [0, 2pi]#.

the number of loops is #(2pi)/(period)= (2pi)/(pi/2)=4#

graph{1/4(x^2+y^2)^2.5-x^4+6x^2y^2-y^4=0 [-10, 10, -5, 5]}