Spherical Coordinates A point can be written in terms of two angles and the distance 1. ρ the distance from the origin to the point Point φ 2. φ from the angle from the positive z axis down to the point ρ 3. θ the angle from the positive x axis to the projection onto xy plane. θ

Converting from Rectangular to Spherical Coordinates red line = green line ρ = z Final Point φ ρ z x tan(φ)= θ y tan(θ)=

Converting from Spherical to Rectangular Coordinates Notice that: z Final Point cos(φ) = φ ρ z sin(φ )= x θ y

Converting from Cylindrical to Spherical Coordinates Length of the red line = r z Final Point φ ρ length of the green line ρ = z r tan(φ)= r θ θ = θ The θ from Cylindrical Coordinates is the same θ in Spherical Coordinates

Converting from Spherical to Cylindrical red line = r z Final Point cos(φ) = φ ρ z sin(φ )= r r θ θ = θ The θ from Spherical Coordinates is the same θ in Cylindrical Coordinates