AnswersPrecalculusPolar Form of Complex Numbers

Graphing Polar Equations Answers

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Two cell phone towers were used to determine the location of an individual calling for assistance. The signal from one tower is represented by r = + sin(θ), and the signal from the other tower by r = 2sin(θ). The points of intersection of the curves are the possible locations of the individual. Which coordinate is one of the possible locations?

Question illustration
A
(Negative StartRoot 3 EndRoot, StartFraction 7 pi Over 6 EndFraction)
Option A
B
(Negative StartRoot 3 EndRoot, StartFraction 5 pi Over 6 EndFraction)
Option B
C
(StartRoot 3 EndRoot, StartFraction 7 pi Over 6 EndFraction)
Option C
D
(StartRoot 3 EndRoot, StartFraction 5 pi Over 6 EndFraction)
Option D
2
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Which equation represents the polar form of x2 + (y – 6)2 = 36?

A
r = 6cos(θ)
B
r = 12cos(θ)
C
r = 6sin(θ)
D
r = 12sin(θ)
3

Which equation represents the polar form of x – y = 0?

A
θ = 0
B
Theta = StartFraction pi Over 4 EndFraction
Option B
C
Theta = StartFraction 3 pi Over 4 EndFraction
Option C
D
θ = π
4

Which graph represents the polar curve r = 3 – 2cos(θ)?

A
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).
Option A
B
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).
Option B
C
On a polar coordinate plane, a circle crosses the x-axis at (0, 0) and (5, pi). It has a convex at (0, 0).
Option C
D
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).
Option D
5

Which graph represents the polar curve r = 5 – cos(θ)?

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

Which graph shape represents the polar curve r = 1 + 4sin(θ)?

A
a cardioid
B
a rose curve
C
a limaçon with an inner loop
D
a limaçon without an inner loop
7

The equation r = 4sin(θ) represents a circle. What is the radius of the circle, and what is the symmetry of the graph?

A
The radius is 2 units, and the graph is symmetric about the line .
Option A
B
The radius is 4 units, and the graph is symmetric about the line .
Option B
C
The radius is 2 units, and the graph is symmetric about the polar axis.
D
The radius is 4 units, and the graph is symmetric about the polar axis.
8

Which graph represents the polar curve r = 4cos(3θ)?

A
On a polar coordinate plane, a rose curve has 8 petals. Four petals are on the x and y-axes.
Option A
B
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).
Option B
C
On a polar coordinate plane, a rose curve has 8 petals. The petals are not on the x- or y-axes.
Option C
D
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).
Option D
9

Which equation represents the rectangular form of ?

Question illustration
A
StartRoot 3 EndRoot x minus y = 0
Option A
B
StartRoot 3 EndRoot x + y = 0
Option B
C
StartRoot 3 EndRoot x minus 3 y = 0
Option C
D
StartRoot 3 EndRoot x + 3 y = 0
Option D
10

Which graph represents points on the polar curve r = 6cos(θ)?

A
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).
Option A
B
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).
Option B
C
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).
Option C
D
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).
Option D

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Graphing Polar Equations Answers — Precalculus