AnswersCUSD Advanced Math A 5.0Graphing Polar Equations

Graphing Polar Equations Answers

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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
2
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Which graph represents the polar curve r = 4sin(θ)?

A
On a polar coordinate plane, a rose curve has 8 petals. The petals are between the x- and y-axes.
Option A
B
On a polar coordinate plane, a circle goes through (0, 0) and (4, StartFraction pi Over 2 EndFraction).
Option B
C
On a polar coordinate plane, a rose curve has 8 petals. Four petals are on the x and y-axes.
Option C
D
On a polar coordinate plane, a circle goes through (0, 0) and (4, 0).
Option D
3

A company designs microphones for use in conference rooms. A new microphone needs to focus on the person speaking and not the voices of other people in the room. Which polar equation would best match the desired audible range of the microphone?

A
r = 3
B
r = 3cos(2θ)
C
r = 3cos(3θ)
D
r = 3 + 3cos(θ)
4

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
5

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
6

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
7

An experiment determines that the polar equation r = 5 + 6cos(θ), where r is in meters, represents the greatest distance between two individuals that still allows them to hear each other speak. Which curve represents this scenario?

A
On a polar coordinate plane, a circle goes through (3.75, StartFraction pi Over 2 EndFraction) and (3.75, StartFraction 3 pi Over 2 EndFraction).
Option A
B
On a polar coordinate plane, a circle goes through (4, StartFraction pi Over 2 EndFraction) and (4, StartFraction 3 pi Over 2 EndFraction).
Option B
C
On a polar coordinate plane, a circle goes through (0, 0) and (11, 0). It has an inner loop at (0, 0).
Option C
D
On a polar coordinate plane, a circle goes through (0, 0) and (12, 0). It has a convex at (0, 0).
Option D
8

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
9

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)
10

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

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