Changing rectangular to cylindrical

In summary, the cylindrical coordinates for the point (-3,3,3) are (3sqrt(2),7pi/4,3), with an angle θ of 3pi/4 in the 2nd quadrant. The correct answer for the angle is 3pi/4, even though the method used in the conversation yielded -pi/4.
  • #1
eurekameh
210
0
Change (-3,3,3) to cylindrical coordinates.
I'm doing r^2 = x^2 + y^2, which I find r = sqrt(18) = 3radical(2)
tan(theta) = 3/-3 = 1, so theta = -pi/4 = 7pi/4.
z = 3
Cylindrical coordinates are (3sqrt(2),7pi/4,3).
Is this right? Correct answer to the homework says 3pi/4 for the angle, for some reason.
 
Physics news on Phys.org
  • #2
eurekameh said:
Change (-3,3,3) to cylindrical coordinates.
I'm doing r^2 = x^2 + y^2, which I find r = sqrt(18) = 3radical(2)
tan(theta) = 3/-3 = 1, so theta = -pi/4 = 7pi/4.
The angle θ is in the 2nd quadrant, so 3[itex]\pi[/itex]/4 is correct.
eurekameh said:
z = 3
Cylindrical coordinates are (3sqrt(2),7pi/4,3).
Is this right? Correct answer to the homework says 3pi/4 for the angle, for some reason.

In the future, when you post a question, use the three-part template.
 

1. What is the formula for converting rectangular coordinates to cylindrical coordinates?

The formula for converting rectangular coordinates (x,y,z) to cylindrical coordinates (r,θ,z) is:
r = √(x^2 + y^2)
θ = tan^-1 (y/x)
z = z

2. How do you visualize the conversion from rectangular to cylindrical coordinates?

To visualize the conversion, imagine a rectangular coordinate system with the x-axis extending horizontally, the y-axis extending vertically, and the z-axis extending perpendicularly. The cylindrical coordinate system is similar, but instead of an x-y plane, there is a r-θ plane where r is the distance from the origin and θ is the angle from the positive x-axis. Z remains the same in both systems.

3. What are the advantages of using cylindrical coordinates over rectangular coordinates?

Cylindrical coordinates are useful for describing shapes that have circular symmetry, such as cylinders or cones. They are also useful for describing motion along a circular path. Additionally, they can simplify certain mathematical calculations, such as finding the volume of a cylinder.

4. Can rectangular coordinates be converted to cylindrical coordinates in reverse?

Yes, rectangular coordinates can be converted to cylindrical coordinates in reverse using the formulas:
x = r cos(θ)
y = r sin(θ)
z = z

5. Are there any limitations to using cylindrical coordinates over rectangular coordinates?

One limitation of using cylindrical coordinates is that they are not as intuitive as rectangular coordinates for describing objects with more complex shapes. Additionally, not all mathematical operations are easily performed in cylindrical coordinates, so rectangular coordinates are often used for more general applications.

Similar threads

Need some help in complex algebra
    • Precalculus Mathematics Homework Help
Replies
14
Views
264
Convert cylindrical coordinate displacement to Cartesian
    • Precalculus Mathematics Homework Help
Replies
1
Views
2K
Solving an equation for ##x## involving inverse circular functions
    • Precalculus Mathematics Homework Help
Replies
15
Views
1K
Solving equations of the form ##a\sin\theta+b\cos\theta = c##
    • Precalculus Mathematics Homework Help
Replies
2
Views
1K
I Cylindrical coordinates -Curvilinear
    • Differential Equations
Replies
1
Views
406
Calculation of moment of inertia of cylindrical surface
    • Calculus and Beyond Homework Help
Replies
4
Views
704
I Determine the Transformation from Cylindrical to Rectangular coordinates
    • Calculus
Replies
5
Views
1K
MHB -11.7.94 Find the rectangular equation
    • General Math
Replies
2
Views
636
I Convert cylindrical coordinates to Cartesian
    • Linear and Abstract Algebra
Replies
6
Views
919
Trigonometric equation of two sines
    • Precalculus Mathematics Homework Help
Replies
8
Views
1K

Hot Threads

Recent Insights

Back
Top