Question

Convert the rectangle coordinates to polar coordinates where r > 0
and 0 ≤ 𝞱 ≤ 2𝛑
(3sqrt3/2,3/2)

Can I have it explained? I know the process to change coordinates, but not when they change the constraints.

Answer 1

Draw the triangle in standard position. You have both x and y positive, so that's in QI. As always,
tanθ = y/x
so here you have
tanθ = (1/2)/ (3√3/2) = 1/(3√3)
so θ ≈ 10.89° ≈ 0.19
But I suspect a typo, and that you really wanted
tanθ = (1/2)/ (√3/2) = 1/√3
so θ = π/6