# Math Help - 2 polar graph questions

1. ## 2 polar graph questions

1.Identify all values of theta for which r=0, and find a range of values of theta that produce one copy of the graph
a) $r=2+4cos3\theta$
my work
$0=2+4cos3\theta$
$\theta= \frac{2\pi}{9}$
$\theta= \frac{4\pi}{9}$
-however, i have no idea to do to find the range to make a copy? can someone tell me the procedure.

2.find a corresponding rectangular equation.
a) $r=3sin\theta$
my work
none
-i understand there are some equations that relate cartesian equations to polar ones. but none of the ones listed in my book list any relevant ones that relate to solving this problem.

All help is appreciated.

2. Originally Posted by dandaman
1.Identify all values of theta for which r=0, and find a range of values of theta that produce one copy of the graph
a) $r=2+4cos3\theta$
my work
$0=2+4cos3\theta$
$\theta= \frac{2\pi}{9}$
$\theta= \frac{4\pi}{9}$
-however, i have no idea to do to find the range to make a copy? can someone tell me the procedure.

2.find a corresponding rectangular equation.
a) $r=3sin\theta$
my work
none
-i understand there are some equations that relate cartesian equations to polar ones. but none of the ones listed in my book list any relevant ones that relate to solving this problem.

All help is appreciated.
For 2.

Note that $\sin\theta=\frac{y}{r}$ from the definition of the sine function, so

$r=3\sin\theta=3\frac{y}{r}$

Which implies that

$r^2=3y$

But, isn't it the case that $r^2=x^2+y^2$ ?