# How do you convert X + Y = 0 into polar form?

Jun 4, 2016

$\theta = - \frac{\pi}{4} , \forall r \in R$

#### Explanation:

The pass equations

{ (x = r cos(theta)), (y = r sin(theta)) :}

substituting

$r \cos \left(\theta\right) + r \sin \left(\theta\right) = 0$
$r \left(\cos \left(\theta\right) + \sin \left(\theta\right)\right) = 0$
$\forall r \to \tan \left(\theta\right) = - 1$

solving

$\theta = - \frac{\pi}{4} + k \pi , k = 0 , 1 , 2 , 3. . .$

then

$\theta = - \frac{\pi}{4} , \forall r \in R$