Question

How do you convert the polar equation `10 sin(θ)` to the rectangular form?

Answer 1

I suppose that your complete equation might be:
`r=10sin(theta)`
To change it in rectangular form you must remember that a point `P` can be represented by:
1) rectangular coordinates `x and y` (on your axes);
2) polar coordinates: a length `r` and an angle `theta`;

In your case we can multiply both sides by `r`:
`r^2=10rsin(theta)`
Substituting for `r^2` and `rsin(theta)` from the above expressions we get:
`x^2+y^2=10y`
in rectangular form.

The graph of your equation is: