Warm-Up 12/05Identify all angles that are coterminal with the given angle. Then give one positive and one negative angle coterminal with the given angle.

1. 165° 2. 165° + 360k°525°; – 195°

+ 2k°

;

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 planePole 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.

Example 1: Graph each point.

a. A(2, 45°)

b. B(– 1.5, )

c. C(3, – 30°)

Example 2: Graph points on a Polar Grid.

a. P(3, )

b. Q(– 3.5, 150°)

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.

Example 4: Graph each polar equation.

a. r = 2

b.

(2, )r

2

2

2

(r, )

r

– 3.5

1

4

Example 5: Find the distance between the pair of points.

A(5, 310°), B(6, 345°)

𝐴𝐵=√𝑟12+𝑟 2

2−2𝑟1𝑟2 cos (𝜃2−𝜃1 )

𝐴𝐵=√52+62−2 (5 ) (6 )cos (345 °−310 ° )

𝐴𝐵≈3.4425

√−1math!

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