Question

Find a rectangular equation that is equivalent to the given polar equation. r^2=8sin(theta) The answer should be set equal to x^2.

Answer 1

my child do you mean r^2= 8sin^(theta)

Answer 2

Possibly? r^2=8sinθ

Answer 3

use the formulas...

\(\large r^2=x^2+y^2 \) and

\(\large x=rcos\theta \) , \(\large y=rsin\theta \)

Answer 4

I've tried to no avail. Since y=rsinθ and we are given 8sinθ, y=8sinθ. Simultaneously, we are given r^2=8sinθ. Using r^2=x^2+y^2, we get 8sinθ=x^2+rsinθ^2. This means that x^2=8sinθ-8sinθ^2=y-y^2. However, x^2=y-y^2 is not the correct answer. What am I doing wrong?