### Cylindrical Coordinates (3-D Graphing)

Graphs one function of the form z=f(r,θ) using cylindrical coordinates in three dimensions.
How to use   ||   Examples   ||   Other Notes

How to use
• Enter a function f1(r,θ) in the text input field marked "f1(r,θ)="
Note: Type "t" for θ in the text input field.
(Example: f1(r,θ)=r)
• Click the "Graph" button (this button also refreshes the graph)
• Rotate the graph by clicking and dragging the mouse on the graph.
• To see two functions graphed simultaneously:
• Enter the second function f2(r,θ) in the text input field marked "f2(r,θ)="
• Click (to its "on" state) the check box next to this input field
• Click the "Graph" button
Note: Type "t" for θ in the text input field.
(Example: f1(r,θ)=r and f2(r,θ)=3+r cos θ)
Up to 3 functions can be graphed simultaneously
• To remove a function from the graph, click (to its "off" state) the check box next to the associated text input field and click the "Graph" button to refresh
• To erase the graph and all input fields, click the "Clear" button
• For each function, there are four input fields which specify bounds on the variables for the function:
• The variable r (the radius) takes values between rmin and rmax, specified by the fields marked "rmin=" and "rmax=".
• The variable θ (the angle, measured counterclockwise in the xy-plane) takes values between θmin*π and θmax*π, with θmin and θmax specified by the fields marked "θmin=" and "θmax=".
• These four text input fields can accept any decimal number input.
The text input fields for functions can accept a wide variety of expressions to represent functions, and the buttons under the graph allow various manipulations of the graph coordinates.
For another way to view surfaces, try the "wireframe" representation.
Examples
 Cone: f1(r,θ)=r Plane: f1(r,θ)=r cos θ Hemisphere: f1(r,θ)=√(25-r2) Paraboloid: f1(r,θ)=r2-5

Other Notes
Surfaces in three dimensions are represented in "faceted hidden surface" form. The facets are not subdivided at intersections of surfaces if more than one surface is drawn, so intersections of surfaces are not precise. The "wireframe" represenation for surfaces, in which the surface is transparent, only draws one surface at a time.