Colts said:I don't understand what r=f(theta,z) means and how to write my answer in that form
##\theta## is given by \theta, not \phi.damabo said:in this case theta is the angle [itex]\phi [/phi] in the equations above
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.
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.
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
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.
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.