Convert to Rectangular r=-3cos(x)

$r = - 3 \cos (x)$

Step 1

Multiply both sides by $r$ .

$r \cdot r = r (- 3 \cos (x))$

Simplify the left side.

Multiply $r$ by $r$ .

$r^{2} = r (- 3 \cos (x))$

Simplify the right side.

Rewrite using the commutative property of multiplication.

$r^{2} = - 3 r \cos (x)$

Step 2

Since $r^{2} = x^{2} + y^{2}$ , replace $r^{2}$ with $x^{2} + y^{2}$ and $r$ with $\sqrt{x^{2} + y^{2}}$ .

$x^{2} + y^{2} = - 3 \sqrt{x^{2} + y^{2}} \cos (x)$