How do you convert r \sin^2 \theta =3 \cos \thetarsin2θ=3cosθ into rectangular form?

1 Answer
Apr 11, 2018

The rectangular form is y^2=3xy2=3x

Explanation:

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

sintheta=y/rsinθ=yr

costheta=x/rcosθ=xr

tantheta=y/xtanθ=yx

and

x^2+y^2=r^2x2+y2=r2

Therefore,

rsin^2theta=3costhetarsin2θ=3cosθ

<=>, r*y^2/r^2=3x/rry2r2=3xr

<=>, y^2=3xy2=3x

This is the equation of a parabola.

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