Which coordinate system is used to represent positions in three dimensions for polar-like mathematics?

Which coordinate system is used to represent positions in three dimensions for polar-like mathematics?

• A. Cylindrical coordinate system
• B. Spherical coordinate system
• C. Cartesian coordinate system
• D. Polar coordinate system

Answer: (B)

In three dimensions, to locate a point in a way that mirrors polar coordinates in a plane, you use spherical coordinates. This system describes a point by a radial distance from the origin and two angles that fix its direction. The typical setup uses r for distance, theta for the azimuth around the z-axis (in the x–y plane), and phi for the angle from the positive z-axis. With these, you can convert to Cartesian coordinates as x = r sin(phi) cos(theta), y = r sin(phi) sin(theta), z = r cos(phi). This combination lets you describe any point by how far it is from the origin and where it points, which is exactly what “polar-like in 3D” is aiming for. Cylindrical coordinates mix a height with a single angle in the plane and don’t provide the full 3D polar description; Cartesian uses rectangular x, y, z, and polar coordinates are inherently 2D.

In three dimensions, to locate a point in a way that mirrors polar coordinates in a plane, you use spherical coordinates. This system describes a point by a radial distance from the origin and two angles that fix its direction. The typical setup uses r for distance, theta for the azimuth around the z-axis (in the x–y plane), and phi for the angle from the positive z-axis. With these, you can convert to Cartesian coordinates as x = r sin(phi) cos(theta), y = r sin(phi) sin(theta), z = r cos(phi). This combination lets you describe any point by how far it is from the origin and where it points, which is exactly what “polar-like in 3D” is aiming for. Cylindrical coordinates mix a height with a single angle in the plane and don’t provide the full 3D polar description; Cartesian uses rectangular x, y, z, and polar coordinates are inherently 2D.