Find an equivalent equation in polar coordinates.
-$$x y = 1$$
A) $2 r ^ { 2 } \sin \theta \cos \theta = 1$
B) $2 r \sin \theta \cos \theta = 1$
C) $\mathrm { r } \sin 2 \theta = 2$
D) $r ^ { 2 } \sin 2 \theta = 2$

Question

Quizplus · Accepted Answer

In polar coordinates, $x = r\cos\theta$ and $y = r\sin\theta$. Substituting these into the given equation $xy = 1$, we get $r\cos\theta \cdot r\sin\theta = 1$, which simplifies to $r^2\sin\theta\cos\theta = 1$. Using the double angle identity $\sin(2\theta) = 2\sin\theta\cos\theta$, we can rewrite the equation as $r^2 \sin(2\theta) = 2$, which matches option D.

Find an Equivalent Equation in Polar Coordinates xy=1x y = 1xy=1

Find an Equivalent Equation in Polar Coordinates $x y = 1$