Convert to Rectangular r=4sin(x)

$r = 4 \sin (x)$

Step 1

Multiply both sides by $r$ .

$r \cdot r = r (4 \sin (x))$

Simplify the left side.

Multiply $r$ by $r$ .

$r^{2} = r (4 \sin (x))$

Simplify the right side.

Rewrite using the commutative property of multiplication.

$r^{2} = 4 r \sin (x)$

Step 2

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

$x^{2} + y^{2} = 4 \sqrt{x^{2} + y^{2}} \sin (x)$