BvU said:
the only answer I see is the az. What did you do to get it ? (It looks to me you are adding z-coordinates)
Thank you. Get the answer and know where's the error.BvU said:Ah, I see. Not only the z coordinate answer differs !
You assume you are given ##(r, \phi, \theta)##. The "usual" order may well be ##(r, \theta, \phi)##. Eureka !
azizlwl said:
Spherical coordinates vectors are a system of representing points in three-dimensional space using three parameters: radius, inclination, and azimuth. In this system, a point is located by measuring the distance from the origin (radius), the angle between the positive z-axis and the line connecting the point to the origin (inclination), and the angle between the positive x-axis and the projection of the point onto the xy-plane (azimuth).
Unlike Cartesian coordinates which use x, y, and z coordinates to represent a point, spherical coordinates use radius, inclination, and azimuth angles. This makes it easier to represent points that are located at a distance from the origin or are located on a curved surface.
One advantage of using spherical coordinates is that it simplifies the representation of points on a spherical or curved surface. It is also useful in physics and engineering applications, such as modeling the movement of objects in space.
To convert from spherical coordinates to Cartesian 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 radius, θ is the inclination angle, and φ is the azimuth angle. To convert from Cartesian coordinates to spherical coordinates, you can use r = √(x² + y² + z²), θ = arccos(z/r), and φ = arctan(y/x).
Spherical coordinates are commonly used in physics, astronomy, and engineering, particularly for applications involving spherical or curved surfaces. Some examples of their applications include mapping the surface of the Earth, modeling planetary orbits, and calculating distances in three-dimensional space.