Convert to Polar Form...3

[nycmathguy]

 

[MathLover1]

19.
y^2 =x^3

In polar coordinates, x=r*cos(θ) and y=r*sin(θ).

Thus, the input can be rewritten as

r^2sin^2(θ)=r^3cos^3 (θ)

r^2sin^2(θ)-r^3cos^3 (θ)=0

Simplify:

r^2(sin^2(θ)-rcos^3(θ))=0

20.

y=x^2

In polar coordinates, x=rcos(θ) and y=rsin(θ).

Thus, the input can be rewritten as

rsin(θ)=(rcos (θ))^2

rsin(θ)=r^2cos^2 (θ)

sin(θ)=rcos^2 (θ)

r=sin(θ)/cos^2(θ)

 

[nycmathguy]

19.
y^2 =x^3

In polar coordinates, x=r*cos(θ) and y=r*sin(θ).

Thus, the input can be rewritten as

r^2sin^2(θ)=r^3cos^3 (θ)

r^2sin^2(θ)-r^3cos^3 (θ)=0

Simplify:

r^2(sin^2(θ)-rcos^3(θ))=0

20.

y=x^2

In polar coordinates, x=rcos(θ) and y=rsin(θ).

Thus, the input can be rewritten as

rsin(θ)=(rcos (θ))^2

rsin(θ)=r^2cos^2 (θ)

sin(θ)=rcos^2 (θ)

r=sin(θ)/cos^2(θ)

Ok. Thank you. I did my best to work out the problems.