1. Holt Geometry 11-Ext Polar Coordinates 11-Ext Polar Coordinates Holt Geometry Lesson Presentation Lesson Presentation

2. Holt Geometry 11-Ext Polar Coordinates Convert between polar and rectangular coordinates. Plot points using polar coordinates. Objectives

3. Holt Geometry 11-Ext Polar Coordinates polar coordinate system pole polar axis Vocabulary

4. Holt Geometry 11-Ext Polar Coordinates In a Cartesian coordinate system, a point is represented by the two coordinates x and y. In a polar coordinate system, a point A is represented by its distance from the origin r, and an angle θ. θ is measured counterclockwise from the horizontal axis to OA. The ordered pair (r, θ) represents the polar coordinates of point A.

5. Holt Geometry 11-Ext Polar Coordinates In a polar coordinate system, the origin is called the pole. The horizontal axis is called the polar axis. You can use the equation of a circle r 2 = x 2 + y 2 and the tangent ratio to convert rectangular coordinates to polar coordinates.

6. Holt Geometry 11-Ext Polar Coordinates Convert (2, 5) to polar coordinates. Example 1: Converting Rectangular Coordinates to Polar Coordinates r 2 = x 2 + y 2 r 2 = 2 2 + 5 2 r 2 = 29 r  5.4 The polar coordinates are (5.4, 68°).

7. Holt Geometry 11-Ext Polar Coordinates Check It Out! Example 1 Convert (4, 1) to polar coordinates. r 2 = x 2 + y 2 r 2 = 4 2 + 1 2 r 2 = 17 r  4.12 The polar coordinates are (4.12, 14°).

8. Holt Geometry 11-Ext Polar Coordinates You can use the relationships x = rcos and y = rsin to convert polar coordinates to rectangular coordinates.

9. Holt Geometry 11-Ext Polar Coordinates Example 2: Converting Polar Coordinates to Rectangular Coordinates Convert (6, 78) to rectangular coordinates. x = r cos  x = 6 cos 78 °  1.25 y = r sin  y = 6 sin 78  5.87 The rectangular coordinates are (1.25, 5.87).

10. Holt Geometry 11-Ext Polar Coordinates Check It Out! Example 2 Convert (4, 60) to rectangular coordinates. x = r cos  x = 4 cos 60 = 2 y = r sin  y = 4 sin 60  3.46 The rectangular coordinates are (2, 3.46).

11. Holt Geometry 11-Ext Polar Coordinates Plot the point (2, 50). Example 3: Plotting Polar Coordinates Step 1 Measure 50 ° counterclockwise from the polar axis. Step 2 Locate the point on the ray that is 2 units from the pole.

12. Holt Geometry 11-Ext Polar Coordinates Check It Out! Example 3 Plot the point (4, 300). Step 1 Measure 300 ° counterclockwise from the polar axis. Step 2 Locate the point on the ray that is 4 units from the pole.

13. Holt Geometry 11-Ext Polar Coordinates Example 4: Graphing Polar Equations Graph r = 3. Make a table of values and plot the points.

14. Holt Geometry 11-Ext Polar Coordinates Check It Out! Example 4 Graph r = 2. 0045135270300 r22222 Make a table of values and plot the points.