Question

Convert the Cartesian equation 2xy = 1 to a polar equation.
(r^2)cosθsinθ = 1
(r^2)sin2θ = 1
(r^22)cos2θ = 1

Answer 1

$\bf \textit{Double Angle Identities} \\\\ sin(2\theta)=2sin(\theta)cos(\theta)\\\\ -------------------------------\\\\ \begin{cases} x=rcos(\theta )\\ y=rsin(\theta ) \end{cases}\qquad 2xy=1\implies 2rcos(\theta )rsin(\theta )=1 \\\\\\ r^2\cdot 2cos(\theta )sin(\theta )=1\implies r^2\cdot sin(2\theta )=1$

Answer 2

Answer:

the second option, $r^2sin2$θ=1

Step-by-step explanation:

x=rcosθ   y=rsinθ   sin2θ=2cosθsinθ

2rcosθrsinθ=1  

divide by r^2 because there are 2 r's

2cosθsinθ=1/r^2

sin2θ=1/r^2 <----multiply each side by r^2

r^2sin2θ=1