Describe the surface in cylindrical coordinates?

In summary, to convert the equation from cartesian coordinates to cylindrical coordinates, substitute x=r*cos(theta) and y=r*sin(theta) in the equation and solve for r. Then, equate r to a function of theta and z, where theta is the angle in polar coordinates and z is the height in cylindrical coordinates.
  • #1
Colts
77
0

Homework Statement


The surface is x^2/y*z=10. Put this into cylidrical coordinates. in the form r=f(theta,z)


Homework Equations


No clue


The Attempt at a Solution


No clue
 
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  • #2
in your book, you will probably find equations for x, for y in terms of theta and z. don't have my book here with me.
 
  • #3
I don't understand what r=f(theta,z) means and how to write my answer in that form
 
  • #4
apparently, this is the conversion from cartesian coordinates (x,y,z) to cilindrical (rho, phi, z):

[itex] x = \rho \cos \varphi [/itex]
[itex]y = \rho \sin \varphi [/itex]
[itex] \rho = \sqrt{x^{2}+y^{2}}[/itex] and

[itex] \varphi = \begin{cases} 0 & \mbox{if } x = 0 \mbox{ and } y = 0\\ \arcsin(\frac{y}{\rho}) & \mbox{if } x \geq 0 \\ -\arcsin(\frac{y}{\rho}) + \pi & \mbox{if } x < 0\\ \end{cases}
[/itex]
 
  • #5
Colts said:
I don't understand what r=f(theta,z) means and how to write my answer in that form

Substitute ##x=r\cos\theta,\, y=r\sin\theta## in the equation and solve it for ##r##.
 
  • #6
f(theta, z) means that you should equate radius to a function of theta and z. in this case theta is the angle [itex]\phi [/phi] in the equations above. this angle, simply put, is the same as the angle in polar coordinates. the only difference between polar coordinates and cilindrical, is that with cilindrical, you have height (z) as well
 
  • #7
damabo said:
in this case theta is the angle [itex]\phi [/phi] in the equations above
##\theta## is given by \theta, not \phi.
 
  • #8
Got it. Thanks guys
 

Related to Describe the surface in cylindrical coordinates?

What are cylindrical coordinates?

Cylindrical coordinates are a type of coordinate system used in mathematics and engineering to describe the location of a point in three-dimensional space. They consist of three components: the radial distance, the azimuthal angle, and the height or vertical distance.

How are cylindrical coordinates different from Cartesian coordinates?

Cylindrical coordinates use a different set of variables to describe a point's location compared to Cartesian coordinates. In cylindrical coordinates, the radial distance (r) is equivalent to the horizontal distance in Cartesian coordinates, the azimuthal angle (θ) is equivalent to the angle of rotation in the horizontal plane, and the height (z) is equivalent to the vertical distance.

What is the formula for converting Cartesian coordinates to cylindrical coordinates?

The formula for converting Cartesian coordinates (x, y, z) to cylindrical coordinates (r, θ, z) is:r = √(x² + y²), θ = arctan(y/x), z = z

How do you describe a surface in cylindrical coordinates?

To describe a surface in cylindrical coordinates, you need to define the relationship between the three components: r, θ, and z. This can be done through an equation or a set of parametric equations that relate the variables to each other.

What are some real-world applications of cylindrical coordinates?

Cylindrical coordinates are commonly used in engineering and physics, particularly in applications involving cylindrical objects such as pipes, cylinders, and turbines. They are also used in navigation and geodesy to describe the location of points on the Earth's surface.

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