# Convert the polar equation to rectangular form.

## Homework Statement

r = 3sin$\theta$

since

x= rcos$\theta$

x = 3sin$\theta$cos$\theta$

and since:

y = rsin$\theta$

y = 3$sin^2\theta$

Then I'm sort of stuck..

LCKurtz
Homework Helper
Gold Member

## Homework Statement

r = 3sin$\theta$

since

x= rcos$\theta$

x = 3sin$\theta$cos$\theta$

and since:

y = rsin$\theta$

y = 3$sin^2\theta$

Then I'm sort of stuck..

You are making it way too difficult. Put ##\sin\theta =\frac y r## in your first equation then see if you can get an xy equation from that.

Dick
Homework Helper

## Homework Statement

r = 3sin$\theta$

since

x= rcos$\theta$

x = 3sin$\theta$cos$\theta$

and since:

y = rsin$\theta$

y = 3$sin^2\theta$

Then I'm sort of stuck..

Try putting sinθ=y/r.

You are making it way too difficult. Put ##\sin\theta =\frac y r## in your first equation then see if you can get an xy equation from that.

Like so:

r = 3sinθ becomes (r=3$\frac{y}{r}$)

= (r =$\sqrt{3y}$) ?

or solving for y, (y = $\frac{r^2}{3}$)

or do you mean something like this:

($\frac{y}{r} = sinθ$) becomes ($\frac{y}{3sinθ} = sinθ$)

= (y = 3sin$^{2}θ$)

Dick
Homework Helper
Like so:

r = 3sinθ becomes (r=3$\frac{y}{r}$)

= (r =$\sqrt{3y}$) ?

or solving for y, (y = $\frac{r^2}{3}$)

or do you mean something like this:

($\frac{y}{r} = sinθ$) becomes ($\frac{y}{3sinθ} = sinθ$)

= (y = 3sin$^{2}θ$)

You also want to use ##r^2=x^2+y^2##. You need to express both ##sin(\theta)## and r in terms of x and y. Try once more.