Convert an Equation from Polar to Rectangular Coordinates
-$$\mathrm { r } ^ { 2 } \sin 2 \theta = 7$$
A) $x y = \frac { 7 } { 2 }$
B) $x y = 7$
C) $y ^ { 2 } = 7$
D) $x ^ { 2 } + y ^ { 2 } = 7$

Question

Quizplus · Accepted Answer

The given equation in polar coordinates is $r^2 \sin 2\theta = 7$. To convert this into rectangular coordinates, we use the identities $r^2 = x^2 + y^2$ and $\sin 2\theta = 2\sin\theta\cos\theta$. Since $\sin\theta = \frac{y}{r}$ and $\cos\theta = \frac{x}{r}$, substituting these into the equation gives $r^2(2\frac{y}{r}\frac{x}{r}) = 7$, which simplifies to $2xy = 7$, or $xy = \frac{7}{2}$.

Convert an Equation from Polar to Rectangular Coordinates - r2sin⁡2θ=7\mathrm { r } ^ { 2 } \sin 2 \theta = 7r2sin2θ=7

Convert an Equation from Polar to Rectangular Coordinates
- $\mathrm { r } ^ { 2 } \sin 2 \theta = 7$