AnswersPrecalculusGraphing Polar Equations

Graphing Polar Equations — Quiz Answers

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1
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Which graph shape represents the polar curve r is equal to 1 plus 4 sine theta ?

A
a rose curve
B
a cardioid
C
a limaçon without an inner loop
D
a limaçon with an inner loop
2
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Which equation represents the polar form of x squared plus open paren y minus 6 close paren squared is equal to 36 ?

A
r is equal to 6 cosine theta
B
r is equal to 12 sine theta
C
r is equal to 12 cosine theta
D
r is equal to 6 sine theta
3

Which graph represents the polar curve r is equal to 4 cosine 3 theta ?

A
Image with description On a polar coordinate plane, a rose curve has 3 petals. One petal goes to (4, 0), another to (4, StartFraction 2 pi Over 3), and another goes to (4, StartFraction 4 pi Over 3 EndFraction).
B
Image with description On a polar coordinate plane, a rose curve has 8 petals. The petals are not on the x- or y-axes.
C
Image with description On a polar coordinate plane, a rose curve has 8 petals. Four petals are on the x and y-axes.
D
Image with description On a polar coordinate plane, a rose curve has 3 petals. One petal goes to (4, StartFraction pi Over 6 EndFraction), another to (4, StartFraction 5 pi Over 6), and another goes to (4, StartFraction 3 pi Over 2 EndFraction).
4

The equation r is equal to 3 cosine 6 theta represents a rose curve. How many petals does the graph contain?

A
3
B
18
C
12
D
6
5

Which graph represents the polar curve r is equal to 4 sine theta ?

A
Image with description On a polar coordinate plane, a rose curve has 8 petals. Four petals are on the x and y-axes.
B
Image with description On a polar coordinate plane, a circle goes through (0, 0) and (4, StartFraction pi Over 2 EndFraction).
C
Image with description On a polar coordinate plane, a circle goes through (0, 0) and (4, 0).
D
Image with description On a polar coordinate plane, a rose curve has 8 petals. The petals are between the x- and y-axes.
6

Which equation represents the polar form of x minus y is equal to 0 ?

A
theta is equal to 0
B
theta is equal to pi
C
theta is equal to 3 pi over 4
D
theta is equal to pi over 4
7

Which graph represents the polar curve r is equal to 3 minus 2 cosine theta ?

A
Image with description On a polar coordinate plane, a circle crosses the x-axis at (0, 0) and (5, pi). It has a convex at (0, 0).
B
Image with description On a polar coordinate plane, a circle crosses the x-axis at (0, 0) and (5, pi). It has an inner loop at (0, 0).
C
Image with description On a polar coordinate plane, a circle crosses the x-axis at (0, 0) and (6, StartFraction 3 pi Over 2 EndFraction). It has an inner loop at (0, 0).
D
Image with description On a polar coordinate plane, a circle crosses the x-axis at (0, 0) and (5, StartFraction 3 pi Over 2 EndFraction). It has an inner loop at (0, 0).
8

Which graph represents points on the polar curve r is equal to 6 cosine theta ?

A
Image with description On a polar coordinate plane, points are at (0, 0), (6, 0), (4, StartFraction pi Over 4 EndFraction), and (4, StartFraction 7 pi Over 4 EndFraction).
B
Image with description On a polar coordinate plane, points are at (0, 0), (6, StartFraction pi Over 2 EndFraction), (4.5, StartFraction pi Over 4 EndFraction), and (4.5, StartFraction 3 pi Over 4 EndFraction).
C
Image with description On a polar coordinate plane, points are at (0, 0), (6, StartFraction 3 pi Over 2 EndFraction), (4.5, StartFraction 5 pi Over 4 EndFraction), and (4.5, StartFraction 7 pi Over 4 EndFraction).
D
Image with description On a polar coordinate plane, points are at (0, 0), (6, pi), (4.5, StartFraction 5 pi Over 4 EndFraction), and (4.5, StartFraction 3 pi Over 4 EndFraction).
9

Which graph represents the polar curve r is equal to 5 minus cosine of theta ?

A
Image with description On a polar coordinate plane, a circle goes through (4, StartFraction pi Over 2 EndFraction), (5, pi), and (6, StartFraction 3 pi Over 2 EndFraction).
B
Image with description On a polar coordinate plane, a circle goes through (6, StartFraction pi Over 2 EndFraction), (5, pi), and (4, StartFraction 3 pi Over 2 EndFraction).
C
Image with description On a polar coordinate plane, a circle goes through (4, 0), (5, StartFraction 3 pi Over 2 EndFraction), and (6, pi).
D
Image with description On a polar coordinate plane, a circle goes through (5, StartFraction pi Over 2 EndFraction), (6, 0), and (4, pi).
10

The equation r is equal to 4 sine theta represents a circle. What is the radius of the circle, and what is the symmetry of the graph?

A
The radius is 4 units, and the graph is symmetric about the polar axis.
B
The radius is 4 units, and the graph is symmetric about the line theta is equal to pi over 2 .
C
The radius is 2 units, and the graph is symmetric about the polar axis.
D
The radius is 2 units, and the graph is symmetric about the line theta is equal to pi over 2 .

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