Warm-Up 12/05 165° + 360k° 525°; – 195°

Rigor: You will learn how graph points and simple graphs with polar coordinates. Relevance: You will be able to use Polar Coordinates to solve real world problems.

9-1 Polar Coordinates

Polar Coordinate System or polar plane Pole is the origin Polar axis is an initial ray from the pole. Polar Coordinates ( r,  ) r is directed distance from the pole  is the directed angle from the polar axis.

In a rectangular coordinate system each point has a unique set of coordinate. This is not true in a polar coordinate system.

Example 3: Find four different pairs of polar coordinates that name point T if – 360°≤  ≤ 360°. (4, 135°) (4, 135°) = (4, 135° – 360°)= (4, – 225°) (4, 135°) = (– 4, 135° + 180°) (4, 135°) = (– 4, 135° – 180°) = (–4, 315°) = (–4, – 45°)

Polar equation is an equation expressed in terms of polar coordinates. For example, r = 2 sin . Polar graph is the set of all points with coordinates ( r,  ) that satisfy a given polar equation.

(2,  ) r  2 2  2 r  –

Example 5: Find the distance between the pair of points. A(5, 310°), B(6, 345°)

math! 9-1 Assignment: TX p538, 2-42 even