Hey my open study isnt working and i need help. How do you convert r = 2a tan(θ)sin(θ) in polar mode to Cartesian or rectangular form? the answer is y2 = x3/(2a - x) but idk how to get that! if you help i will write you an awesome testimony! please help!!

Question

mertsj · Answer

Posted for bridgetx516x

anonymous · Answer

$$
r=2a\tan(\theta)\sin(\theta)\\;\
x=r\cos(\theta)\qquad y=r\sin(\theta)\qquad\tan(\theta)={y\over x}\
r=2a{y\over x}{y\over r}\
r^2=2a{y^2\over x}\
x^2+y^2={2ay^2\over x}\
\boxed{x^3+xy^2=2ay^2}
$$

anonymous · Answer

$$x^3=y^2(2a-x)\\implies\boxed{y^2=\Large{x^3\over 2a-x}}$$

anonymous · Answer

posted for @bridgetx516x http://www-groups.dcs.st-and.ac.uk/~history/Curves/Cissoid.html

mertsj · Answer

ty on behalf of the asker

anonymous · Answer

@Mertsj I did reply in a message to the asker.

mertsj · Answer

Ty

anonymous · Answer

np