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Vocabulary polar coordinate system pole polar axis polar coordinates polar equation polar graph.

Date post: 20-Jan-2016
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Page 1: Vocabulary polar coordinate system pole polar axis polar coordinates polar equation polar graph.

• polar coordinate system

• pole

• polar axis

• polar coordinates

• polar equation

• polar graph

Page 2: Vocabulary polar coordinate system pole polar axis polar coordinates polar equation polar graph.

Graph Polar Coordinates

A. Graph S(1, 200°).

Because = 200o, sketch the terminal side of a 200o angle with the polar axis as its initial side. Because r = 1, plot a point 1 unit from the pole along the terminal side of this angle.

Answer:

Page 3: Vocabulary polar coordinate system pole polar axis polar coordinates polar equation polar graph.

Graph Polar Coordinates

B. Graph .

Because , sketch the terminal side of a

angle with the polar axis as its initial side. Because r is

negative, extend the terminal side of the angle in the

opposite direction and plot a point 2 units from the

pole along this extended ray.

Page 4: Vocabulary polar coordinate system pole polar axis polar coordinates polar equation polar graph.

Answer:

Graph Polar Coordinates

Page 5: Vocabulary polar coordinate system pole polar axis polar coordinates polar equation polar graph.

Graph Polar Coordinates

Because = –90o, sketch the terminal side of a –90o angle with the polar axis as its initial side. Because r = 4, plot a point 4 units from the pole along the terminal side of this angle.

C. Graph M(4, –90°).

Answer:

Page 6: Vocabulary polar coordinate system pole polar axis polar coordinates polar equation polar graph.

Graph H(3, 120o).

A.

B.

C.

D.

Page 7: Vocabulary polar coordinate system pole polar axis polar coordinates polar equation polar graph.

Graph Points on a Polar Grid

A. Graph on a polar grid.

Because , sketch the terminal side of a

angle with the polar axis as its initial side. Because r =

3, plot a point 3 units from the pole along the terminal

side of the angle.

Page 8: Vocabulary polar coordinate system pole polar axis polar coordinates polar equation polar graph.

Graph Points on a Polar Grid

Answer:

Page 9: Vocabulary polar coordinate system pole polar axis polar coordinates polar equation polar graph.

Graph Points on a Polar Grid

B. Graph Q(–2, –240°) on a polar grid.

Because = –240o, sketch the terminal side of a –240o angle with the polar axis as its initial side. Because r is negative, extend the terminal side of the angle in the opposite direction and plot a point 2 units from the pole along this extended ray.

Page 10: Vocabulary polar coordinate system pole polar axis polar coordinates polar equation polar graph.

Graph Points on a Polar Grid

Answer:

Page 11: Vocabulary polar coordinate system pole polar axis polar coordinates polar equation polar graph.

Graph on a polar grid.

A.

B.

C.

D.

Page 12: Vocabulary polar coordinate system pole polar axis polar coordinates polar equation polar graph.

Multiple Representations of Polar Coordinates

Find four different pairs of polar coordinates that name point S if –360° < θ < 360°.

Page 13: Vocabulary polar coordinate system pole polar axis polar coordinates polar equation polar graph.

Multiple Representations of Polar Coordinates

One pair of polar coordinates that name point S is (2, 210°). The other three representations are as follows.

(2, 210°) = (2, 210o – 360°) Subtract 360° from .

= (2, –150o)

(2, 210°) = (–2, 210° – 180°) Replace r with –r and subtract.

= (–2, 30°) 180° from .

Page 14: Vocabulary polar coordinate system pole polar axis polar coordinates polar equation polar graph.

Multiple Representations of Polar Coordinates

Answer: (2, –150°), (2, 210°), (–2, 30°), (–2, –330°)

(2, 210°) = (2, –150°)

= (–2, –150° – 180°) Replace r with –r and subtract

= (–2, –330°) 180° from .

Page 15: Vocabulary polar coordinate system pole polar axis polar coordinates polar equation polar graph.

Find four different pairs of polar coordinates that name point W if –360o < < 360o.

A. (7, 30°), (7, 150°), (7, 210°), (7, 330°)

B. (7, –60°), (7, 330°), (–7, 120°), (–7, 300°)

C. (7, –30°), (7, 330°), (–7, 150°), (–7, –210°)

D. (7, –150°), (7, 330°), (–7, 30°), (–7, 210°)

Page 16: Vocabulary polar coordinate system pole polar axis polar coordinates polar equation polar graph.

Graph Polar Equations

A. Graph the polar equation r = 2.5.

The solutions of r = 2.5 are ordered pairs of the form (2.5, ), where is any real number.

The graph consists of all points that are 2.5 units from the pole, so the graph is a circle centered at the origin with radius 2.5.

Answer:

Page 17: Vocabulary polar coordinate system pole polar axis polar coordinates polar equation polar graph.

Graph Polar Equations

B. Graph the polar equation .

The solutions of are ordered pairs of the form

, where r is any real number. The graph

consists of all points on the line that makes an angle of

with the positive polar axis.

Page 18: Vocabulary polar coordinate system pole polar axis polar coordinates polar equation polar graph.

Answer:

Graph Polar Equations

Page 19: Vocabulary polar coordinate system pole polar axis polar coordinates polar equation polar graph.

Graph

A.

B.

C.

D.

Page 20: Vocabulary polar coordinate system pole polar axis polar coordinates polar equation polar graph.
Page 21: Vocabulary polar coordinate system pole polar axis polar coordinates polar equation polar graph.

Find the Distance Between Polar Coordinates

A. AIR TRAFFIC An air traffic controller is tracking two airplanes that are flying at the same altitude. The coordinates of the planes are A(8, 60°) and B(4, 300°), where the directed distance is measured in miles. Sketch a graph of this situation.

Airplane A is located 8 miles from the pole on the terminal side of the angle 60°, and airplane B is located 4 miles from the pole on the terminal side of the angle 300°, as shown.

Page 22: Vocabulary polar coordinate system pole polar axis polar coordinates polar equation polar graph.

Answer:

Find the Distance Between Polar Coordinates

Page 23: Vocabulary polar coordinate system pole polar axis polar coordinates polar equation polar graph.

Find the Distance Between Polar Coordinates

B. AIR TRAFFIC An air traffic controller is tracking two airplanes that are flying at the same altitude. The coordinates of the planes are A(8, 60°) and B(4, 300°), where the directed distance is measured in miles. How far apart are the two airplanes?

Use the Polar Distance Formula.

Polar Distance Formula

Page 24: Vocabulary polar coordinate system pole polar axis polar coordinates polar equation polar graph.

Answer: about 10.6 miles

Find the Distance Between Polar Coordinates

(r2, 2) = (4, 300°) and(r1, 1) = (8, 60°)

The planes are about 10.6 miles apart.

Page 25: Vocabulary polar coordinate system pole polar axis polar coordinates polar equation polar graph.

BOATS Two sailboats can be described by the coordinates (9, 60o) and (5, 320o), where the directed distance is measured in miles. How far apart are the boats?

A. about 5.4 miles

B. about 10.7 miles

C. about 11.0 miles

D. about 12.9 miles

Page 26: Vocabulary polar coordinate system pole polar axis polar coordinates polar equation polar graph.

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