Question #8b24f

Question

1704 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-03-10T12:12:32

$r = \pm \frac{3}{2} sin (2 θ)$ $r=pm3/2sin(2theta)$

The pass equations are

${(x=rcostheta),(y=rsintheta):}$

so

$(r^2)^3=3^2r^4cos^2thetasin^2theta$ or

$r^2=3^2cos^2theta sin^2theta$ or

$r=pm 3costheta sin theta$ ---------(*)

using $sin(a+b)=sin acos b+cosa sinb$ and making $a=b$

we get at

$sin(2a)=2sina cosa$ then $sin theta cos theta = 1/2 sin(2theta)$

substituting into (*) we obtain

$r=pm3/2sin(2theta)$

Attached a plot.

enter image source here