Question

In Exercises \(47-52,\) convert the point from spherical coordinates to cylindrical coordinates. $$ (18, \pi / 3, \pi / 3) $$

Short answer

The conversion of spherical coordinates (18, π/3, π/3) to cylindrical coordinates gives (r', φ', z') ≈ (15.59, π/3, 9).

Step-by-step solution

Identify Spherical Coordinates

The spherical coordinates given in the problem are (r, θ, φ) = (18, π/3, π/3).

Apply Conversion Formulas

Now apply the conversion formulas to convert spherical coordinates (r, θ, φ) to cylindrical coordinates (r', φ', z'). Follow the subsequent conversion formulas: r' = r sinφ, φ' = θ, and z' = r cosφ.

Calculate Cylindrical Coordinates

Put the identified spherical coordinates values in the conversion formulas: r' = 18 sin(π/3), φ' = π/3, and z' = 18 cos(π/3). After calculation, we get the cylindrical coordinates (r', φ', z') ≈ (15.59, π/3, 9).