How to Apply Basic Operations to Matrices
How to Solve Linear Systems that Have More than Two Equations
Adding and Subtracting Vectors

How to Plot Cylindrical Coordinates

Cylindrical coordinates are simply polar coordinates with the addition of a vertical z-axis extending from the origin. While a polar coordinate pair is of the form

image0.png

with cylindrical coordinates, every point in space is assigned a set of coordinates of the form

image1.png

The polar coordinate system assigns a pairing of values to every point on the plane. However, these values aren’t dependent on two perpendicular axes (though these axes are often drawn in to make the graph more readable). The key axis is the horizontal axis.

Here’s what you need to know:

  • The variable r measures the distance from the z-axis to that point.

  • The variable

    image2.png
  • measures angular distance from the horizontal axis. This angle is measured in radians rather than degrees, so that

    image3.png
  • The variable z measures the distance from that point to the xy-plane.

When plotting cylindrical coordinates, plot the first coordinates

image4.png

just as you would for polar coordinates. Then plot the z-coordinate.

image5.jpg

This figure shows you how to plot the point

image6.png

in cylindrical coordinates:

  1. Count 3 units to the right of the origin on the horizontal axis (as you would when plotting polar coordinates).

  2. Travel counterclockwise along the arc of a circle until you reach the line drawn at a π/2-angle from the horizontal axis (again, as with polar coordinates).

  3. Count 2 units above the plane and plot your point there.

  • Add a Comment
  • Print
  • Share
blog comments powered by Disqus
How to Solve Differential Equations Using Op Amps
Solving Separable Differential Equations
Checking Differential Equation Solutions
How to Use a Partial Derivative to Measure a Slope in Three Dimensions
Evaluating Triple Integrals
Advertisement

Inside Dummies.com