Question

Help making this--> r=3sin2theta<-- into x and y to graph? I'm stuck.

Answer 1

@whpalmer4 ?

Answer 2

@surjithayer

Answer 3

\[x=r \cos \theta, y=r \sin \theta ,\]
\[x^2+y^2=r^2\left( \cos ^2\theta+\sin ^2 \theta \right)=r^2\]
\[r=3 \sin 2 \theta =3*2 \sin \theta \cos \theta \]
\[r^3=6 r \sin \theta * r \cos \theta\]
\[\left( \sqrt{x^2+y^2} \right)^3=6 y x\]
\[\left( x^2+y^2 \right)^3=36x^2y^2\]

Answer 4

Point of clarification: is it
\[r = 3\sin 2\theta\]or\[r = 3\sin^2\theta\]?

Answer 5

if \[r=3 \sin ^2\theta =3*\frac{ y^2 }{ r^2 },r^3=3 y^2,\left( \sqrt{x^2+y^2} \right)^3=3y^2\]
\[\left( x^2+y^2 \right)^3=9y^4\]

Answer 6

No, the 2 was big beside theta, but the answer choices are 4 graphs.. how do I plug what you gave me into a graph?

Answer 7

@phi ?

Answer 8

@jim_thompson5910

Answer 9

@sourwing ?

Answer 10

to find the graph (by hand) is make a table
angle 2*angle r=3 sin(2A)
0 0 0
15 30 1.5
22.5 45 2.1
30 60 2.6
45 90 3
60 120 2.6
67.5 135 2.1
75 150 1.5
90 180 0


you should keep going for the angles in the other quadrants (you should get the same pattern)

to plot these points, draw a line at each angle. make each line as long a "r"
draw a smooth curve connecting the tips of the lines