Download presentation

Presentation is loading. Please wait.

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

20
Need Help? If you are ever in need of assistance type in the following equation: See the next slide

21
Help is on the way…

Similar presentations

OK

MA 242.003 Day 45 – March 18, 2013 Section 9.7: Cylindrical Coordinates Section 12.8: Triple Integrals in Cylindrical Coordinates.

MA 242.003 Day 45 – March 18, 2013 Section 9.7: Cylindrical Coordinates Section 12.8: Triple Integrals in Cylindrical Coordinates.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google