ZedCar said:
tiny-tim said:Infinite!
A sketch in cylindrical coordinates for z=6 represents a 3-dimensional graph of the function z=6 in cylindrical coordinates. This means that the z-value, or height, of the graph is always equal to 6, while the x and y values, or radius and angle, can vary.
To convert from cartesian coordinates (x,y,z) to cylindrical coordinates (r,θ,z), use the following equations:
The range of values for r is from 0 to infinity, as it represents distance and cannot be negative. The range of values for θ is from 0 to 2π, as it represents angles in radians.
To plot a sketch in cylindrical coordinates, first determine the range of values for r and θ. Then, plot points on the xy-plane using these values, with z always equal to the given constant. Connect the points to create a smooth curved graph, representing the function in cylindrical coordinates.
Cylindrical coordinates are commonly used in engineering and physics to represent objects with cylindrical symmetry, such as pipes, cylinders, and rotating objects. They are also used in navigation and map-making, as well as in polar coordinates to represent locations on a sphere.