Ch 9 Polar Coordinates and Complex numbers
description
Transcript of Ch 9 Polar Coordinates and Complex numbers
![Page 1: Ch 9 Polar Coordinates and Complex numbers](https://reader031.fdocuments.in/reader031/viewer/2022012919/56816725550346895ddbb567/html5/thumbnails/1.jpg)
Ch 9 Polar Coordinates and Complex numbers
L9.2 Graphs of Polar equations
![Page 2: Ch 9 Polar Coordinates and Complex numbers](https://reader031.fdocuments.in/reader031/viewer/2022012919/56816725550346895ddbb567/html5/thumbnails/2.jpg)
![Page 3: Ch 9 Polar Coordinates and Complex numbers](https://reader031.fdocuments.in/reader031/viewer/2022012919/56816725550346895ddbb567/html5/thumbnails/3.jpg)
You must be able to match the graph with its name and its equation.
![Page 4: Ch 9 Polar Coordinates and Complex numbers](https://reader031.fdocuments.in/reader031/viewer/2022012919/56816725550346895ddbb567/html5/thumbnails/4.jpg)
Classical Curves
![Page 5: Ch 9 Polar Coordinates and Complex numbers](https://reader031.fdocuments.in/reader031/viewer/2022012919/56816725550346895ddbb567/html5/thumbnails/5.jpg)
Petals of a rose
• n-petalled rose if n is odd, or a 2n-petalled rose if n is even. If n is rational but not an integer, a rose-like shape may form but with overlapping petals. Note that these equations never define a rose with 2, 6, 10, 14, etc. petals. The variable a represents the length of the petals of the rose.
![Page 6: Ch 9 Polar Coordinates and Complex numbers](https://reader031.fdocuments.in/reader031/viewer/2022012919/56816725550346895ddbb567/html5/thumbnails/6.jpg)
![Page 7: Ch 9 Polar Coordinates and Complex numbers](https://reader031.fdocuments.in/reader031/viewer/2022012919/56816725550346895ddbb567/html5/thumbnails/7.jpg)
Classwork
![Page 8: Ch 9 Polar Coordinates and Complex numbers](https://reader031.fdocuments.in/reader031/viewer/2022012919/56816725550346895ddbb567/html5/thumbnails/8.jpg)
Classical Curves
![Page 9: Ch 9 Polar Coordinates and Complex numbers](https://reader031.fdocuments.in/reader031/viewer/2022012919/56816725550346895ddbb567/html5/thumbnails/9.jpg)
![Page 10: Ch 9 Polar Coordinates and Complex numbers](https://reader031.fdocuments.in/reader031/viewer/2022012919/56816725550346895ddbb567/html5/thumbnails/10.jpg)
Classical Curves
![Page 11: Ch 9 Polar Coordinates and Complex numbers](https://reader031.fdocuments.in/reader031/viewer/2022012919/56816725550346895ddbb567/html5/thumbnails/11.jpg)
![Page 12: Ch 9 Polar Coordinates and Complex numbers](https://reader031.fdocuments.in/reader031/viewer/2022012919/56816725550346895ddbb567/html5/thumbnails/12.jpg)
Classical CurvesCardioid – a special case of the limacon family of curves
![Page 13: Ch 9 Polar Coordinates and Complex numbers](https://reader031.fdocuments.in/reader031/viewer/2022012919/56816725550346895ddbb567/html5/thumbnails/13.jpg)
Cardoid
![Page 14: Ch 9 Polar Coordinates and Complex numbers](https://reader031.fdocuments.in/reader031/viewer/2022012919/56816725550346895ddbb567/html5/thumbnails/14.jpg)
Classical Curves
![Page 15: Ch 9 Polar Coordinates and Complex numbers](https://reader031.fdocuments.in/reader031/viewer/2022012919/56816725550346895ddbb567/html5/thumbnails/15.jpg)
![Page 16: Ch 9 Polar Coordinates and Complex numbers](https://reader031.fdocuments.in/reader031/viewer/2022012919/56816725550346895ddbb567/html5/thumbnails/16.jpg)
Classwork - HandoutHomework – page 565 11-22
![Page 19: Ch 9 Polar Coordinates and Complex numbers](https://reader031.fdocuments.in/reader031/viewer/2022012919/56816725550346895ddbb567/html5/thumbnails/19.jpg)
Experiment with your calculator.
• Try graphing the classic polar graphs.• Experiment with different values for a and b
and determine what effect each has on the graph.
• Experiment with the sin and cos and determine what effect each has on the graph.
• Write your equation on your handout chart and sketch its graph below.
![Page 20: Ch 9 Polar Coordinates and Complex numbers](https://reader031.fdocuments.in/reader031/viewer/2022012919/56816725550346895ddbb567/html5/thumbnails/20.jpg)
Now lets try the following problems.
• Copy the questions on your notebook paper.• Write your answers.• Check for correctness.
![Page 22: Ch 9 Polar Coordinates and Complex numbers](https://reader031.fdocuments.in/reader031/viewer/2022012919/56816725550346895ddbb567/html5/thumbnails/22.jpg)
• Practice Master 9-2
![Page 23: Ch 9 Polar Coordinates and Complex numbers](https://reader031.fdocuments.in/reader031/viewer/2022012919/56816725550346895ddbb567/html5/thumbnails/23.jpg)
![Page 24: Ch 9 Polar Coordinates and Complex numbers](https://reader031.fdocuments.in/reader031/viewer/2022012919/56816725550346895ddbb567/html5/thumbnails/24.jpg)
![Page 25: Ch 9 Polar Coordinates and Complex numbers](https://reader031.fdocuments.in/reader031/viewer/2022012919/56816725550346895ddbb567/html5/thumbnails/25.jpg)
![Page 26: Ch 9 Polar Coordinates and Complex numbers](https://reader031.fdocuments.in/reader031/viewer/2022012919/56816725550346895ddbb567/html5/thumbnails/26.jpg)
![Page 27: Ch 9 Polar Coordinates and Complex numbers](https://reader031.fdocuments.in/reader031/viewer/2022012919/56816725550346895ddbb567/html5/thumbnails/27.jpg)
![Page 28: Ch 9 Polar Coordinates and Complex numbers](https://reader031.fdocuments.in/reader031/viewer/2022012919/56816725550346895ddbb567/html5/thumbnails/28.jpg)
![Page 29: Ch 9 Polar Coordinates and Complex numbers](https://reader031.fdocuments.in/reader031/viewer/2022012919/56816725550346895ddbb567/html5/thumbnails/29.jpg)
![Page 30: Ch 9 Polar Coordinates and Complex numbers](https://reader031.fdocuments.in/reader031/viewer/2022012919/56816725550346895ddbb567/html5/thumbnails/30.jpg)
![Page 31: Ch 9 Polar Coordinates and Complex numbers](https://reader031.fdocuments.in/reader031/viewer/2022012919/56816725550346895ddbb567/html5/thumbnails/31.jpg)