Question

Convert the following point from spherical to rectangular coordinates:

Answer 1

To convert a point from spherical to rectangular coordinates, use the formulas x = r sin(θ) cos(φ), y = r sin(θ) sin(φ), and z = r cos(θ).

Step-by-step explanation:

To convert a point from spherical to rectangular coordinates, you can use the formulas x = r sin(θ) cos(φ), y = r sin(θ) sin(φ), and z = r cos(θ), where r is the radial coordinate, θ is the polar angle, and φ is the azimuthal angle.

For example, let's say the spherical coordinates of a point are (r, θ, φ) = (5, π/4, π/6). We can substitute these values into the above formulas to find the rectangular coordinates.

x = 5 sin(π/4) cos(π/6) = √2 * √3 / 4 ≈ 0.966.

y = 5 sin(π/4) sin(π/6) = √2 * 1 / 4 ≈ 0.354.

z = 5 cos(π/4) = √2 * √2 / 2 ≈ 3.536.