1. ANSWERS

3. Check Homework

4. PRE Lesson 8.1 & 8.2 Polar Coordinates & their Graphs Objectives: To understand the relationship between rectangular and polar coordinates.

5. CHAPTER OVERVIEW In this chapter, we study polar coordinates—a new way of describing the location of points in a plane. A coordinate system is a method for specifying the location of a point in the plane. We are familiar with rectangular (or Cartesian) coordinates.

7. RECTANGULAR COORDINATE SYSTEM In rectangular coordinates, the location of a point is given by an ordered pair (x, y), which gives the distance of the point to two perpendicular axes. Using rectangular coordinates is like describing a location in a city by saying that it’s at the corner of 2 nd Street and 4 th Avenue.

8. However, we might also describe this same location by saying that it’s 1½ miles northeast of City Hall.

9. So, instead of specifying the location with respect to a grid of streets and avenues, we specify it by giving its distance and direction from a fixed reference point. ◦ That is what we do in the polar ◦ coordinate system.

10. In polar coordinates, the location of a point is given by an ordered pair (r, θ) where: ◦ r is the distance from the origin (or pole). ◦ θ is the angle from the positive x-axis.

11.  To change from polar to rectangular coordinates, use the formulas:

12. You still NEeD This

13. Find rectangular coordinates for the point that has polar coordinates (4, 2π/3).

14. Find rectangular coordinates for the point that has polar coordinates (-4, 5π/2).

15. Where is this when graph?

16.  To change from rectangular to polar coordinates, use the formulas: RECTANGULAR  POLAR

17. Find polar coordinates for the point that has rectangular coordinates (2, –2).

18. You still NEeD This

19. Find polar coordinates for the point that has rectangular coordinates (2, –2).

20. Find polar coordinates for the point that has rectangular coordinates.

21. You still NEeD This

22. Find polar coordinates for the point that has rectangular coordinates.

23. Classwork: Polar Coordinate/Vector Worksheet: 1-16 all