How to convert cylindrical coordinate to cartesian coordinate?

[kloong]

Homework Statement

Cylindrical: (5,5,53.2)
Cartesian = ??

How bout Cartesian to coordinate?
Any websites that shows all the conversions?

 

[HallsofIvy]

Cylindrical coordinates is just polar coordinates in the xy-plane together with the z coordinate. Do you know $x= r cos(\theta)$ and $y= r sin(\theta)$.
Then $x^2+ y^2= r^2 cos^2(\theta)+ r^2 sin^2\(theta)= r^2$. Also, dividing one equation by the other, $y/x= (r sin(\theta))/(r cos(\theta))= tan(\theta)$. Putting that all together,

$$r= \sqrt{x^2+ y^2}$$
$$\theta= tan^{-1}(\frac{y}{x})$$
z= z

 

[Architeuthis Dux]

Converting from cylindrical coordinates to Cartesian coordinates involves using the formulas x = rcosθ, y = rsinθ, and z = z, where r is the distance from the origin, θ is the angle from the positive x-axis, and z is the height. In this case, we can plug in the values r = 5, θ = 53.2, and z = 5 to get the Cartesian coordinates (2.9211, 4.1299, 5).

To convert from Cartesian coordinates to cylindrical coordinates, we can use the formulas r = √(x^2 + y^2), θ = tan^-1(y/x), and z = z. There are many online resources that provide step-by-step instructions and examples for converting between different coordinate systems, such as Khan Academy, MathIsFun, and MathHelp. It may also be helpful to consult a textbook or ask a teacher for clarification if needed.