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11-Ext

Polar Coordinates. 11-Ext. Lesson Presentation. Holt Geometry. Objectives. Convert between polar and rectangular coordinates. Plot points using polar coordinates. Vocabulary. polar coordinate system pole polar axis.

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11-Ext

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  1. Polar Coordinates 11-Ext Lesson Presentation Holt Geometry

  2. Objectives Convert between polar and rectangular coordinates. Plot points using polar coordinates.

  3. Vocabulary polar coordinate system pole polar axis

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

  5. You can use the equation of a circle r2 = x2 + y2 and the tangent ratio to convert rectangular coordinates to polar coordinates. In a polar coordinate system, the origin is called the pole. The horizontal axis is called the polar axis.

  6. Example 1: Converting Rectangular Coordinates to Polar Coordinates Convert (2, 5) to polar coordinates. r2 = x2 + y2 r2 = 22 + 52 r2 = 29 r 5.4 The polar coordinates are (5.4, 68°).

  7. Check It Out! Example 1 Convert (4, 1) to polar coordinates. r2 = x2 + y2 r2 = 42 + 12 r2 = 17 r 4.12 The polar coordinates are (4.12, 14°).

  8. You can use the relationships x = rcos and y = rsin to convert polar coordinates to rectangular coordinates.

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

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

  11. Example 3: Plotting Polar Coordinates Plot the point (2, 50). 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. 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. Example 4: Graphing Polar Equations Graph r = 3. Make a table of values and plot the points.

  14. Check It Out! Example 4 Graph r = 2. Make a table of values and plot the points.

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