In polar coordinate system, what is the distance from point (2, - π / 6) to line PSIN (A-30) = 1? P is Rou in polar coordinates, and a is angular alpha

In polar coordinate system, what is the distance from point (2, - π / 6) to line PSIN (A-30) = 1? P is Rou in polar coordinates, and a is angular alpha

The polar coordinates are transformed into rectangular coordinates: point (root 3, - 1), and the linear equation is: root 3y-x-2 = 0
Using the formula of distance from point to line, d = root 3 + 1

When the perpendicular foot is h (2, π 3), the polar coordinate equation of the line L is ⊙___ ．

As shown in the figure, the pole o is perpendicular to the straight line L, and the perpendicular foot is h. let the polar coordinates of any point of the straight line l be (ρ, θ). In the right triangle ohm, ∠ Hom = ρ - π 3, oh = omcos ∠ Hom,  ρ cos (θ - π 3) = 2 or expand to: ρ cos θ + 3 ρ sin θ - 4 = 0. Therefore, the answer is: ρ cos (θ - π 3) = 2 or ρ cos θ + 3 ρ sin θ - 4 = 0

Mathematical problems in polar coordinates
The parameter equation of curve C in Cartesian coordinate system is x = 2cos α, y = 2 + 2Sin α (α is the parameter). If the polar coordinate system is established with the origin as the pole, the positive half axis of X axis as the polar axis and the length unit unchanged, the polar coordinate equation of curve C is_________
The answer is ρ = 4sin θ
Can you give me the process?

Let the polar coordinates of C be (ρ, θ) x = ρ * cos θ = 2cos α cos α = ρ * cos θ / 2 y = ρ * sin θ = 2 + 2Sin α sin α = (ρ * sin θ - 2) / 2, and cos α ^ 2 + sin α ^ 2 = 1 ρ ^ 2 * cos θ ^ 2 / 4 + [ρ ^ 2 * sin θ ^ 2 + 4-4 (ρ * sin θ)] / 4 = 1 ρ ^ 2 * cos θ ^ 2 + ρ ^ 2 * sin θ ^ 2 + 4-4 (ρ