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

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google