Question 1

Select the graph of the polar equation using symmetry,zeros,maximum r-values,and any other additional points.​ $r = 5 \cos \theta$ ​

Accepted Answer

A) Symmetric with respect to polar axis Circle with radius 2.5
​   
B) Symmetric with respect to polar axis Circle with radius 2.5
​   
C) Symmetric with respect to polar axis Circle with radius 2.5
​   
D) Symmetric with respect to polar axis Circle with radius 2.5
​   
E) Symmetric with respect to polar axis Circle with radius 2.5
​   
A) Symmetric with respect to polar axis Circle with radius 2.5
​   
B) Symmetric with respect to polar axis Circle with radius 2.5
​   
C) Symmetric with respect to polar axis Circle with radius 2.5
​   
D) Symmetric with respect to polar axis Circle with radius 2.5
​   
E) Symmetric with respect to polar axis Circle with radius 2.5
​

Question 2

Select the graph of the polar equation using symmetry,zeros,maximum r-values,and any other additional points.​ $$r = \csc \theta$$ ​

Accepted Answer

A)  $$y = 1 \Rightarrow \text { Line }$$   
B)  $$y = 1 \Rightarrow \text { Line }$$   
C)  $$y = 1 \Rightarrow \text { Line }$$   
D)  $$y = 1 \Rightarrow \text { Line }$$   
E)  $$y = 1 \Rightarrow \text { Line }$$   
A)  $$y = 1 \Rightarrow \text { Line }$$   
B)  $$y = 1 \Rightarrow \text { Line }$$   
C)  $$y = 1 \Rightarrow \text { Line }$$   
D)  $$y = 1 \Rightarrow \text { Line }$$   
E)  $$y = 1 \Rightarrow \text { Line }$$

Question 3

Select the graph of the polar equation using symmetry,zeros,maximum r-values,and any other additional points.​ $r = 2 ( 1 - \sin \theta )$ ​

Accepted Answer

A) Symmetric with respect to $\frac { \pi } { 2 }$ $\begin{array} { l } 
| r | = 4 \text { when } \theta = \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 2 }
\end{array}$ ​   
B) Symmetric with respect to $\frac { \pi } { 2 }$ $\begin{array} { l } 
| r | = 4 \text { when } \theta = \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 2 }
\end{array}$ ​   
C) Symmetric with respect to $\frac { \pi } { 2 }$ $$\begin{array} { l } 
| r | = 4 \text { when } \theta = \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 2 }
\end{array}$$ ​   
D) Symmetric with respect to $$\frac { \pi } { 2 }$$ $$\begin{array} { l } 
| r | = 4 \text { when } \theta = \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 2 }
\end{array}$$ ​   
E) Symmetric with respect to $$\frac { \pi } { 2 }$$ $$\begin{array} { l } 
| r | = 4 \text { when } \theta = \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 2 }
\end{array}$$ ​   
A) Symmetric with respect to $\frac { \pi } { 2 }$ $\begin{array} { l } 
| r | = 4 \text { when } \theta = \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 2 }
\end{array}$ ​   
B) Symmetric with respect to $\frac { \pi } { 2 }$ $\begin{array} { l } 
| r | = 4 \text { when } \theta = \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 2 }
\end{array}$ ​   
C) Symmetric with respect to $\frac { \pi } { 2 }$ $$\begin{array} { l } 
| r | = 4 \text { when } \theta = \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 2 }
\end{array}$$ ​   
D) Symmetric with respect to $$\frac { \pi } { 2 }$$ $$\begin{array} { l } 
| r | = 4 \text { when } \theta = \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 2 }
\end{array}$$ ​   
E) Symmetric with respect to $$\frac { \pi } { 2 }$$ $$\begin{array} { l } 
| r | = 4 \text { when } \theta = \frac { 3 \pi } { 2 } \
r = 0 \text { when } \theta = \frac { \pi } { 2 }
\end{array}$$ ​

Question 4

Select the correct graph of the polar equation.Describe your viewing window.​ $$r = \frac { 7 } { 4 }$$ ​

Accepted Answer

A) ​   $$\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 5 \
X _ { \max } = 5 \
X _ { s c l } = 1 \
Y _ { \min } = - 5 \
Y _ { \max } = 5 \
Y _ { s c l } = 1
\end{array}$$ 
B) ​   $$\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 5 \
X _ { \max } = 5 \
X _ { s c l } = 1 \
Y _ { \min } = - 5 \
Y _ { \max } = 5 \
Y _ { s c l } = 1
\end{array}$$ 
C) ​   $$\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 5 \
X _ { \max } = 5 \
X _ { s c l } = 1 \
Y _ { \min } = - 5 \
Y _ { \max } = 5 \
Y _ { s c l } = 1
\end{array}$$ 
D) ​   $$\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 5 \
X _ { \max } = 5 \
X _ { s c l } = 1 \
Y _ { \min } = - 5 \
Y _ { \max } = 5 \
Y _ { s c l } = 1
\end{array}$$ 
E) ​   $$\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 5 \
X _ { \max } = 5 \
X _ { s c l } = 1 \
Y _ { \min } = - 5 \
Y _ { \max } = 5 \
Y _ { s c l } = 1
\end{array}$$ 
A) ​   $$\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 5 \
X _ { \max } = 5 \
X _ { s c l } = 1 \
Y _ { \min } = - 5 \
Y _ { \max } = 5 \
Y _ { s c l } = 1
\end{array}$$ 
B) ​   $$\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 5 \
X _ { \max } = 5 \
X _ { s c l } = 1 \
Y _ { \min } = - 5 \
Y _ { \max } = 5 \
Y _ { s c l } = 1
\end{array}$$ 
C) ​   $$\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 5 \
X _ { \max } = 5 \
X _ { s c l } = 1 \
Y _ { \min } = - 5 \
Y _ { \max } = 5 \
Y _ { s c l } = 1
\end{array}$$ 
D) ​   $$\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 5 \
X _ { \max } = 5 \
X _ { s c l } = 1 \
Y _ { \min } = - 5 \
Y _ { \max } = 5 \
Y _ { s c l } = 1
\end{array}$$ 
E) ​   $$\begin{array} { l } 
\theta _ { \min } = 0 \
\theta _ { \max } = 2 \pi \
\theta _ { s t e p } = \pi / 24 \
X _ { \min } = - 5 \
X _ { \max } = 5 \
X _ { s c l } = 1 \
Y _ { \min } = - 5 \
Y _ { \max } = 5 \
Y _ { s c l } = 1
\end{array}$$

Question 5

Select the graph of the polar equation using symmetry,zeros,maximum r-values,and any other additional points.​ $$r = \frac { 8 } { 2 \sin \theta - 3 \cos \theta }$$ ​

Accepted Answer

A)  $$y = \frac { 3 } { 2 } x + 4 \Rightarrow \text { Line }$$ ​   
B)  $$y = \frac { 3 } { 2 } x + 4 \Rightarrow \text { Line }$$ ​   
C)  $$y = \frac { 3 } { 2 } x + 4 \Rightarrow \text { Line }$$ ​   
D)  $$y = \frac { 3 } { 2 } x + 4 \Rightarrow \text { Line }$$ ​   
E)  $$y = \frac { 3 } { 2 } x + 4 \Rightarrow \text { Line }$$ ​   
A)  $$y = \frac { 3 } { 2 } x + 4 \Rightarrow \text { Line }$$ ​   
B)  $$y = \frac { 3 } { 2 } x + 4 \Rightarrow \text { Line }$$ ​   
C)  $$y = \frac { 3 } { 2 } x + 4 \Rightarrow \text { Line }$$ ​   
D)  $$y = \frac { 3 } { 2 } x + 4 \Rightarrow \text { Line }$$ ​   
E)  $$y = \frac { 3 } { 2 } x + 4 \Rightarrow \text { Line }$$ ​

Question 6

Select the graph of the polar equation using symmetry,zeros,maximum r-values,and any other additional points.​ $$r = 3 + 7 \cos \theta$$ ​

Accepted Answer

A) Symmetric with respect to the polar axis $$| r | = 10 \text { when } \theta = 0$$ ​   
B) Symmetric with respect to the polar axis $$| r | = 10 \text { when } \theta = 0$$ ​   
C) Symmetric with respect to the polar axis $$| r | = 10 \text { when } \theta = 0$$ ​   
D) Symmetric with respect to the polar axis $$| r | = 10 \text { when } \theta = 0$$ ​   
E) Symmetric with respect to the polar axis $$| r | = 10 \text { when } \theta = 0$$ ​   
A) Symmetric with respect to the polar axis $$| r | = 10 \text { when } \theta = 0$$ ​   
B) Symmetric with respect to the polar axis $$| r | = 10 \text { when } \theta = 0$$ ​   
C) Symmetric with respect to the polar axis $$| r | = 10 \text { when } \theta = 0$$ ​   
D) Symmetric with respect to the polar axis $$| r | = 10 \text { when } \theta = 0$$ ​   
E) Symmetric with respect to the polar axis $$| r | = 10 \text { when } \theta = 0$$ ​

Question 7

Select the graph of $$r = 3 \cos \theta$$ over the interval.Describe the part of the graph obtained in this case.​ $$0 \leq \theta \leq \pi$$ ​

Accepted Answer

A) ​   Upper half of circle 
B) ​   Upper half of circle 
C) ​   Upper half of circle 
D) ​   Upper half of circle 
E) ​   Upper half of circle 
A) ​   Upper half of circle 
B) ​   Upper half of circle 
C) ​   Upper half of circle 
D) ​   Upper half of circle 
E) ​   Upper half of circle

Question 8

Select the graph of the polar equation using symmetry,zeros,maximum r-values,and any other additional points.​ $$r = 4 - 5 \cos \theta$$ ​

Accepted Answer

A) Symmetric with respect to polar axis $| r | = 9$ when $\theta = \pi$
$r = 0 \text { when } \theta = \frac { \pi } { 3 } , \frac { 5 \pi } { 3 }$ ​   
B) Symmetric with respect to polar axis $| r | = 9$ when $\theta = \pi$
$r = 0 \text { when } \theta = \frac { \pi } { 3 } , \frac { 5 \pi } { 3 }$ ​   
C) Symmetric with respect to polar axis $| r | = 9$ when $\theta = \pi$
$r = 0 \text { when } \theta = \frac { \pi } { 3 } , \frac { 5 \pi } { 3 }$ ​   
D) Symmetric with respect to polar axis $| r | = 9$ when $\theta = \pi$
$r = 0 \text { when } \theta = \frac { \pi } { 3 } , \frac { 5 \pi } { 3 }$ ​   
E) Symmetric with respect to polar axis $| r | = 9$ when $\theta = \pi$
$r = 0 \text { when } \theta = \frac { \pi } { 3 } , \frac { 5 \pi } { 3 }$ ​   
A) Symmetric with respect to polar axis $| r | = 9$ when $\theta = \pi$
$r = 0 \text { when } \theta = \frac { \pi } { 3 } , \frac { 5 \pi } { 3 }$ ​   
B) Symmetric with respect to polar axis $| r | = 9$ when $\theta = \pi$
$r = 0 \text { when } \theta = \frac { \pi } { 3 } , \frac { 5 \pi } { 3 }$ ​   
C) Symmetric with respect to polar axis $| r | = 9$ when $\theta = \pi$
$r = 0 \text { when } \theta = \frac { \pi } { 3 } , \frac { 5 \pi } { 3 }$ ​   
D) Symmetric with respect to polar axis $| r | = 9$ when $\theta = \pi$
$r = 0 \text { when } \theta = \frac { \pi } { 3 } , \frac { 5 \pi } { 3 }$ ​   
E) Symmetric with respect to polar axis $| r | = 9$ when $\theta = \pi$
$r = 0 \text { when } \theta = \frac { \pi } { 3 } , \frac { 5 \pi } { 3 }$ ​

Question 9

Select the graph of the polar equation using symmetry,zeros,maximum r-values,and any other additional points.​ $$r = 1$$ ​

Accepted Answer

A) Symmetric with respect to $$\theta = \frac { \pi } { 2 }$$ ,polar axis,pole Circle with radius $$r = 1$$
​   
B) Symmetric with respect to $$\theta = \frac { \pi } { 2 }$$ ,polar axis,pole Circle with radius $$r = 1$$
​   
C) Symmetric with respect to $$\theta = \frac { \pi } { 2 }$$ ,polar axis,pole Circle with radius $$r = 1$$
​   
D) Symmetric with respect to $$\theta = \frac { \pi } { 2 }$$ ,polar axis,pole Circle with radius $$r = 1$$
​   
E) Symmetric with respect to $$\theta = \frac { \pi } { 2 }$$ ,polar axis,pole Circle with radius $$r = 1$$
​   
A) Symmetric with respect to $$\theta = \frac { \pi } { 2 }$$ ,polar axis,pole Circle with radius $$r = 1$$
​   
B) Symmetric with respect to $$\theta = \frac { \pi } { 2 }$$ ,polar axis,pole Circle with radius $$r = 1$$
​   
C) Symmetric with respect to $$\theta = \frac { \pi } { 2 }$$ ,polar axis,pole Circle with radius $$r = 1$$
​   
D) Symmetric with respect to $$\theta = \frac { \pi } { 2 }$$ ,polar axis,pole Circle with radius $$r = 1$$
​   
E) Symmetric with respect to $$\theta = \frac { \pi } { 2 }$$ ,polar axis,pole Circle with radius $$r = 1$$
​

Exam 67: Graphs of Polar Equations

Select the graph of the polar equation using symmetry,zeros,maximum r-values,and any other additional points.​ r=5cos⁡θr = 5 \cos \thetar=5cosθ ​

Select the graph of the polar equation using symmetry,zeros,maximum r-values,and any other additional points.​ r=csc⁡θr = \csc \thetar=cscθ ​

Select the graph of the polar equation using symmetry,zeros,maximum r-values,and any other additional points.​ r=2(1−sin⁡θ)r = 2 ( 1 - \sin \theta )r=2(1−sinθ) ​

Select the correct graph of the polar equation.Describe your viewing window.​ r=74r = \frac { 7 } { 4 }r=47​ ​

Select the graph of the polar equation using symmetry,zeros,maximum r-values,and any other additional points.​ r=82sin⁡θ−3cos⁡θr = \frac { 8 } { 2 \sin \theta - 3 \cos \theta }r=2sinθ−3cosθ8​ ​

Select the graph of the polar equation using symmetry,zeros,maximum r-values,and any other additional points.​ r=3+7cos⁡θr = 3 + 7 \cos \thetar=3+7cosθ ​

Select the graph of r=3cos⁡θr = 3 \cos \thetar=3cosθ over the interval.Describe the part of the graph obtained in this case.​ 0≤θ≤π0 \leq \theta \leq \pi0≤θ≤π ​

Select the graph of the polar equation using symmetry,zeros,maximum r-values,and any other additional points.​ r=4−5cos⁡θr = 4 - 5 \cos \thetar=4−5cosθ ​

Select the graph of the polar equation using symmetry,zeros,maximum r-values,and any other additional points.​ r=1r = 1r=1 ​

Rectangular Coordinates

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Linear Equations in Two Variables

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Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

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Polynomial and Synthetic Division

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Zeros of Polynomial Functions

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Nonlinear Inequalities

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Introduction to Conics Parabolas

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Filters

Select the graph of the polar equation using symmetry,zeros,maximum r-values,and any other additional points. $r = 5 \cos \theta$

Select the graph of the polar equation using symmetry,zeros,maximum r-values,and any other additional points. $r = \csc \theta$

Select the graph of the polar equation using symmetry,zeros,maximum r-values,and any other additional points. $r = 2 ( 1 - \sin \theta )$

Select the correct graph of the polar equation.Describe your viewing window. $r = \frac { 7 } { 4 }$

Select the graph of the polar equation using symmetry,zeros,maximum r-values,and any other additional points. $r = \frac { 8 } { 2 \sin \theta - 3 \cos \theta }$

Select the graph of the polar equation using symmetry,zeros,maximum r-values,and any other additional points. $r = 3 + 7 \cos \theta$

Select the graph of $r = 3 \cos \theta$ over the interval.Describe the part of the graph obtained in this case. $0 \leq \theta \leq \pi$

Select the graph of the polar equation using symmetry,zeros,maximum r-values,and any other additional points. $r = 4 - 5 \cos \theta$

Select the graph of the polar equation using symmetry,zeros,maximum r-values,and any other additional points. $r = 1$