Answer:
r²sinθcosθ = 1 OR r²sin2θ = 2
Step-by-step explanation:
Polar coordinates are represented in of the radius r and angle θ.
In the x axis:
x = rcosθ
Along the y-axis:
y = rsinθ
Rectangular coordinate to polar coordinate will be:
(x, y) = (rcosθ, rsinθ)
To convert the equation xy = 1 to polar coordinate, we will substitute the value of x and y in its polar form into the given equation to have:
(rcosθ)(rsinθ) = 1
r²sinθcosθ = 1...(1)
From the trigonometry identity
Sin2θ = 2sinθcosθ
Sinθcosθ = sin2θ/2...(2)
Substituting equation 2 into 1:
r²(sin2θ/2) = 1
r²sin2θ = 2
