1. 11.7 Day 1 Cylindrical Coordinates

2. Comparing Cartesian and cylindrical coordinates

3. Note: these are just polar coordinates with a z coordinate (z is a vertical component)

4. Conversion formulas from cylindrical to rectangular coordinates

5. Converting between cylindrical coordinates and rectangular (Cartesian) Note: these formulas must be memorized

6. Example 1 Convert the point (r, ө, z) = (4, 5π/6, 3)
to rectangular coordinates.

7. Solution to example 1

8. Example 2 _ Convert the point (x, y, z) = (1, √3 , 2)
to cylindrical coordinates.

10. Cylindrical coordinates are usually more convenient for representing cylindrical surfaces as they often result in simpler equations.

11. Vertical planes containing the z-axis and horizontal planes also have simple cylindrical coordinate equations

12. Example 3 a
Find an equation in cylindrical coordinates for the surfaces represented by the rectangular equation:

13. Solution to 3a From the preceding section, you know that x2 + y2 = 4z2
is a “double napped” cone with its axis along the z-axis as shown.
If you replace x2 + y2 with r2, the equation in cylindrical
Coordinates is r2 = 4z2
x2 + y2 = 4z2 Rectangular equation
r2 = 4z Cylindrical equation

14. Example 3b
Find an equation in cylindrical coordinates for the surfaces represented by the rectangular equation:

15. Solution to 3b

16. Example 4
Find an equation in rectangular coordinates for the surface represented by the cylindrical equation:
Identify the surface
r2cos2θ +z2 +1 = 0

17. z y x

18. Changing between coordinates on the TI 89
Press 2nd 5 (math) – 4 matrices – L Vecor ops
To polar, to cynd To convert rectangular to Polar (2 D) or cylindrical (3D)
[1,2] to Polar (to expressed with a triangle)
[1,2,3] to Cylind

19. Note: Homework do the assignment sheet
plus the activity on the class website.
This is a polar bear in rectangular form
Bonus material on the
next slides

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