Given spherical and cylindarical coordinates, draw each one

In summary, spherical and cylindrical coordinates are two different systems for representing points in three-dimensional space. They are useful in many scientific and engineering applications, particularly in solving problems involving curved surfaces or objects. To convert between these coordinates, specific equations can be used. Examples of when these coordinates would be used include astronomy and electromagnetic theory. To draw a point given its coordinates, specific steps must be followed based on the system used.
  • #1
sinned4789
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Homework Statement


part 1) draw 3(R-hat) + 3(theta-hat) + 3(phi-hat)
part 2) draw 3(r-hat) + 3(theta-hat) + 3(z-hat)


Homework Equations





The Attempt at a Solution


aren't these the same thing? just 3 in each of the x, y, and z directions in cartesian coordinates.
 
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  • #2
Absolutely not. Look up the wiki pages on spherical and cylindrical coordinates.
 

FAQ: Given spherical and cylindarical coordinates, draw each one

1. What are spherical and cylindrical coordinates?

Spherical and cylindrical coordinates are two different systems for representing points in three-dimensional space. Spherical coordinates use the parameters of radius, inclination, and azimuth to locate a point in space, while cylindrical coordinates use the parameters of radius, height, and angle.

2. How do you convert between spherical and cylindrical coordinates?

To convert from spherical to cylindrical coordinates, you can use the following equations:

x = r*sin(θ)*cos(ϕ)
y = r*sin(θ)*sin(ϕ)
z = r*cos(θ)
where r is the radius, θ is the inclination, and ϕ is the azimuth. To convert from cylindrical to spherical coordinates, use the following equations:

r = √(x^2 + y^2)
θ = arctan(y/x)
ϕ = arccos(z/r)
where x, y, and z are the coordinates in the cylindrical system.

3. Why are spherical and cylindrical coordinates useful?

Spherical and cylindrical coordinates are useful in many scientific and engineering applications, particularly in problems involving three-dimensional space. They can make it easier to visualize and solve problems involving curved surfaces or objects, such as spheres or cylinders.

4. Can you give an example of when spherical and cylindrical coordinates would be used?

Spherical coordinates are commonly used in astronomy, as they are well-suited for describing the positions of stars and planets in space. Cylindrical coordinates are often used in electromagnetic theory, as they can simplify calculations involving cylindrical objects like wires or antennas.

5. How would you draw a point given its spherical or cylindrical coordinates?

To draw a point given its spherical coordinates, you would first plot the radius on the z-axis, then rotate the point by the inclination angle θ, and finally rotate it by the azimuth angle ϕ. To draw a point given its cylindrical coordinates, you would first plot the radius on the x-y plane, then extend a line from the origin to the height of the point, and finally rotate it by the angle around the z-axis.

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