How do you convert #r \sin^2 \theta =3 \cos \theta# into rectangular form?

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Answer 1 · 2018-04-11T08:17:00

The rectangular form is #y^2=3x#

To convert from polar coordinates to rectangular coordinates, apply the following

#sintheta=y/r#

#costheta=x/r#

#tantheta=y/x#

and

#x^2+y^2=r^2#

Therefore,

#rsin^2theta=3costheta#

#<=>#, #r*y^2/r^2=3x/r#

#<=>#, #y^2=3x#

This is the equation of a parabola.

graph{(y^2-3x)=0 [-3.375, 16.625, -4.36, 5.64]}