- #1
seang
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I have no idea how to do this. I've tried a lot of things but I can never reduce it to solely cartesian coordinates. Is there any hard fast procedure to conversions like this? thanks.
The formula for converting rx in spherical coordinates to cartesian is:
x = r * sin(phi) * cos(theta)
y = r * sin(phi) * sin(theta)
z = r * cos(phi)
Where r is the distance from the origin, phi is the angle from the positive z-axis, and theta is the angle from the positive x-axis.
To determine the values of r, phi, and theta for a point in spherical coordinates, you will need to know the distance of the point from the origin, the angle between the point and the positive z-axis, and the angle between the point and the positive x-axis. These values can be found using trigonometric functions or by using a coordinate system diagram.
Yes, negative coordinates can exist in spherical coordinates. The distance from the origin (r) can be negative, indicating that the point is in the opposite direction of the positive z-axis. The angles phi and theta can also be negative, indicating that the point is in the opposite direction of the positive x-axis and positive z-axis, respectively.
One limitation of using spherical coordinates is that they are not as intuitive as cartesian coordinates. It can be difficult to visualize the location of a point using r, phi, and theta values. Additionally, spherical coordinates are not suitable for all types of calculations, such as those involving complex shapes or objects with changing coordinates.
Spherical coordinates are commonly used in various fields of science and engineering, such as physics, astronomy, and navigation. They are particularly useful for describing the location of objects in 3D space, such as stars in the night sky or the position of a ship at sea. They are also used in computer graphics to represent the position of objects in 3D models.