The letters x and y represent rectangular coordinates. Write the following equation using polar coordinates (r, θ).
xy=1
possible solutions:
2rsinθcosθ=1
r²sinθcosθ=1
rsin2θ=2
r²sin2θ=2
I chose: r²sinθcosθ=1
Am I wrong?
looks good to me
To rewrite the equation xy = 1 using polar coordinates (r, θ), we need to express the variables x and y in terms of r and θ.
We know that in rectangular coordinates, x = r cosθ and y = r sinθ.
Substituting these values into the equation xy = 1:
(r cosθ)(r sinθ) = 1
r²(cosθ)(sinθ) = 1
r²sinθcosθ = 1
So, you are correct in choosing r²sinθcosθ = 1 as the equation in polar coordinates. Well done!