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

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.

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.

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

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.

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.

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

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

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

Where is this when graph?

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

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

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

Find polar coordinates for the point that has rectangular coordinates.

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Find polar coordinates for the point that has rectangular coordinates.

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