Polar Coordinates And Complex Numbers Worksheets With Answers - Math 611b Page 4
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50Polar Coordinates (9.1)
1. Explain why a point in the polar plane can’t be labelled using a unique ordered pair (r, 2 ).
2. Explain how to graph (r, 2 ) if r < 0 and 2 > 0.
3. Name two values of 2 such that ( ! 4, 2 ) represents the same point as (4, 120°).
4. Graph each point:
d) D( ! 2, 13 B /6)
b) B(2.5, !B /6) c) C( ! 3, ! 120°)
a) A(1, 135°)
f) F(1, B /2)
g) G(1/2, 3 B /4)
h) H(5/2, ! 210°)
i) I(2, ! 90°)
e) E(2, 30°)
5. Name four different pairs of polar coordinates for each point:
a) ( ! 2, B /6)
c) ( ! 1, B /3)
b) (1.5, 180°)
d) (4, 315°)
6. Graph each polar equation:
b) 2 = !B /3
e) 2 = 5 B /4
f) 2 = ! 150°
a) r = 1
c) r = 3.5
d) r = 1.5
7. Find the distance between the points with the given polar coordinates:
(1, B /6) and P
(5,3 B /4)
(1.3, ! 47°) and P
( ! 3.6, ! 62°)
a) P
b) P
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8. When designing web-sites with circular graphics, it is often convenient to use polar coordinates. If the
origin is at the centre of the screen, what are the polar equations of the lines that cut the region into the
eight congruent slices shown.
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