How do you graph #r=-8sin3theta#?

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Answer 1 · 2016-12-27T21:58:32

It has a 3 blade propeller shape.

I tried graphing #r = -8sin(3theta)# in both polar and Cartesian coordinates; neither is easy.

I used WolframAlpha to convert to functions of #theta#:

#r = 8sin^3(theta) - 24sin(theta)cos^2(theta)#

Multiply both sides by #r^3#:

#r^4 = 8r^3sin^3(theta) - 24rsin(theta)r^2cos^2(theta)#

Applying the polar to rectangular conversion equations:

#(x^2 + y^2)^2 = 8y^2 - 24y(x^2)#

Here is the graph:

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