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seto6
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Homework Statement
do we only use spherical and cylindrical coordinates for triple integrals? or for double too?
thanks for your replies in advance
Spherical coordinates use a radius, an angle from the positive z-axis, and an angle from the positive x-axis to describe a point in three-dimensional space. Cylindrical coordinates use a radius, an angle from the positive x-axis, and a height to describe a point in three-dimensional space.
Spherical coordinates are useful for describing points in space that have a radial symmetry, such as a sphere or a planet. Cylindrical coordinates are better suited for describing objects with a cylindrical symmetry, such as a cylinder or a tornado.
To convert from spherical coordinates to cylindrical coordinates, use the following equations:
x = ρsinθcosφ
y = ρsinθsinφ
z = ρcosθ
To convert from cylindrical coordinates to spherical coordinates, use the following equations:
ρ = √(x^2 + y^2 + z^2)
θ = arctan(y/x)
φ = arccos(z/ρ)
Yes, it is possible to use a combination of spherical and cylindrical coordinates in the same problem. This is often done when describing more complex objects that do not have a simple symmetry.
Yes, spherical and cylindrical coordinates are commonly used in many areas of science, such as physics, astronomy, and engineering. They are especially useful in fields that deal with three-dimensional objects and systems, as they provide a more intuitive way to describe and analyze them.