### Home > APCALC > Chapter 12 > Lesson 12.3.1 > Problem12-93

12-93.

Rewrite the polar equation $r ( \theta ) = \frac { 4 } { \sqrt { \operatorname { cos } ( 2 \theta ) } }$ in rectangular form. State the domain of $r(θ)$. Describe the graph and explain how the domain relates to the graph.

$r\sqrt{\cos(2\theta)}=4$

$r^2\cos(2\theta)=16$

$r^2(2\cos^2(\theta)-1)=16$

$2r^2\cos^2(\theta)-r^2=16$

$2x^2-(x^2+y^2)=16$

For the domain, $\cos(2θ)>0$.