The letters r and θ represent polar coordinates. Write the equation using rectangular coordinates (x, y).
-$$\mathrm { r } = 1 + 2 \sin \theta$$
A) $\sqrt { x ^ { 2 } + y ^ { 2 } } = x ^ { 2 } + y ^ { 2 } + 2 y$
B) $x ^ { 2 } + y ^ { 2 } = \sqrt { x ^ { 2 } + y ^ { 2 } } + 2 y$
C) $x ^ { 2 } + y ^ { 2 } = \sqrt { x ^ { 2 } + y ^ { 2 } } + 2 x$
D) $\sqrt { x ^ { 2 } + y ^ { 2 } } = x ^ { 2 } + y ^ { 2 } + 2 x$

Question

Quizplus · Accepted Answer

In polar coordinates, $r = \sqrt{x^2 + y^2}$ and $\sin \theta = \frac{y}{r}$. Substituting these into the given equation $r = 1 + 2\sin \theta$ gives $x^2 + y^2 = \sqrt{x^2 + y^2} + 2y$.

The Letters R and θ Represent Polar Coordinates r=1+2sin⁡θ\mathrm { r } = 1 + 2 \sin \thetar=1+2sinθ

The Letters R and θ Represent Polar Coordinates $\mathrm { r } = 1 + 2 \sin \theta$