So r sinƟ = 2alexmolinavr6 said:Homework Statement
cylindrical coordinates: r=2cscƟ, give both rectangular and spherical cordinates
Homework Equations
I know this:
From rectangular to cylinder
z=z r2=x2+y2 tanƟ=y/x
From Cyl to rectangle
x=cosƟ y=sinƟ z=z
From cyl to spherical
Ɵ=Ɵ ρ2=x2+y2+z2 ɸ=sin-1r/ρ
From Spherical to cylindrical
Ɵ=Ɵ r=ρsinɸ z=ρcosɸ
The Attempt at a Solution
so far what I have is
r=2/sinƟ
can anyone please help me, I got stuck
Mark44 said:What does the equation r sinƟ = 2 represent geometrically?
Mark44 said:What does the equation r sinƟ = 2 represent geometrically?
alexmolinavr6 said:From Cyl to rectangle
x=cosƟ y=sinƟ z=z
Mark44 said:What can you replace rsinƟ with? BTW your conversion formulas from cylindrical to rectangular are wrong.
A cylindrical coordinate system is a type of coordinate system used in mathematics and physics to describe the position of a point in three-dimensional space. It is based on a cylindrical shape, with a vertical axis and a circular base.
The three coordinates used in cylindrical coordinates are the radial distance (r), the azimuthal angle (θ), and the height or elevation (z). These coordinates represent the distance from the origin, the angle from a reference direction, and the height above the xy-plane, respectively.
To convert from Cartesian coordinates (x, y, z) to cylindrical coordinates (r, θ, z), you can use the following formulas:
r = √(x² + y²)
θ = tan⁻¹(y/x)
z = z
One advantage of using cylindrical coordinates is that it simplifies certain mathematical equations, particularly those involving circular or cylindrical shapes. It also allows for a more intuitive representation of certain physical phenomena, such as rotating objects or cylindrical structures.
Cylindrical coordinates are commonly used in engineering and physics to describe the motion and forces of rotating objects, such as turbines and propellers. They are also used in describing the shape and orientation of cylindrical structures, such as pipes and cylindrical tanks. In addition, they are used in various fields of science, such as astronomy and geology, to describe the position and movement of objects in space or on the Earth's surface.