a) Find the Cartesian coordinates for the polar coordinate (3, - 7phi/6)Given polar coordinate (r, θ) = (3, - 7phi/6)The Cartesian coordinate can be obtained as follows:x = r cos θ and y = r sin θ.x = 3 cos (-7π/6) and y = 3 sin (-7π/6)x = 3 (-√3/2) - 3/2 and y = 3 (-1/2)x = - (3√3 + 3)/2 and y = - (3/2)Hence, the Cartesian coordinate is (- (3√3 + 3)/2, - (3/2)).b) Find polar coordinates for the Cartesian coordinate (√3– 1) where r > 0, and θ > 0.Given Cartesian coordinate (x, y) = (√3– 1) and r > 0, and θ > 0.Using x = r cos θ and y = r sin θ:r = √(x² + y²)r = √((√3– 1)² + y²)r = √(4 - 2√3 + y²)θ = tan⁻¹(y/(√3– 1))The polar coordinates are: (r, θ) = [√(4 - 2√3 + y²), tan⁻¹(y/(√3– 1))]c) Give three alternate versions for the polar point (2, 5phi/3)Given polar coordinate (r, θ) = (2, 5π/3)If θ < 0, then adding 2π to θ gives the alternate polar coordinates with positive angle: (r, θ + 2π) = (2, 5π/3 + 2π) = (2, 11π/3)If r < 0, then adding π to θ gives the alternate polar coordinates with reversed sign of radius: (r, θ + π) = (-2, 5π/3 + π) = (-2, 8π/3)If both r < 0 and θ < 0, then adding π to θ and 2π to θ gives the alternate polar coordinates with reversed sign of radius and positive angle: (r, θ + π + 2π) = (-2, 5π/3 + π + 2π) = (-2, 2π/3).