Deck 8: Polar Coordinates; Vectors

Question 1

Plot the point given in polar coordinates.

- $$\left( - 2 , \frac { 9 \pi } { 4 } \right)$$

A)


B)

C)


D)

Answer 1

Question 2

Plot the point given in polar coordinates.

- $$\left( 4 , \frac { - 5 \pi } { 4 } \right)$$
11ed81e9_d221_d939_a8e7_a59319399610_TB7697_

A)


B)

C)


D)

Answer 2

Question 3

Plot the point given in polar coordinates.

- $$\left( 3 , \frac { 7 \pi } { 6 } \right)$$

A)


B)

C)


D)

Answer 3

Question 4

Match the point in polar coordinates with either A, B, C, or D on the graph.

- $$\left( - 3 , - \frac { \pi } { 3 } \right)$$

A) A
B) B
C) C
D) D

Question 5

Plot the point given in polar coordinates.

- $\left(2,-\frac{\pi}{4}\right)$

A)


B)

C)


D)

Question 6

Solve the problem.

Question 7

Plot the point given in polar coordinates.

- $$\left( 4,315 ^ { \circ } \right)$$

A)


B)

C)


D)

Question 8

Plot the point given in polar coordinates.

- $$\left( 4,30 ^ { \circ } \right)$$

A)


B)

C)


D)

Question 9

Plot the point given in polar coordinates.

- $$\left( 2 , \frac { 9 \pi } { 4 } \right)$$

A)


B)

C)


D)

Question 10

Plot the point given in polar coordinates.

- $\left[-2, \frac{-3 \pi}{4}\right.$

A)


B)

C)


D)

Question 11

Match the point in polar coordinates with either A, B, C, or D on the graph.

- $\left[-3, \frac{\pi}{3}\right]$

A) A
B) B
C) C
D) D

Question 12

The polar coordinates of a point are given. Find the rectangular coordinates of the point.

- $\left( 7 , \frac { 2 \pi } { 3 } \right)$

A) $\left( - \frac { 7 } { 2 } , \frac { 7 \sqrt { 3 } } { 2 } \right)$
B) $\left( \frac { 7 } { 2 } , \frac { - 7 \sqrt { 3 } } { 2 } \right)$
C) $\left( - \frac { 7 } { 2 } , \frac { - 7 \sqrt { 3 } } { 2 } \right)$
D) $\left( \frac { 7 } { 2 } , \frac { 7 \sqrt { 3 } } { 2 } \right)$

Question 13

Plot the point given in polar coordinates.

- $$\left( 2,45 ^ { \circ } \right)$$

A)


B)

C)


D)

Question 14

Plot the point given in polar coordinates.

- $\left[5, \frac{5 \pi}{3}\right)$

A)

B)

C)


D)

Question 15

Plot the point given in polar coordinates.

- $$\left( 2,0 ^ { \circ } \right)$$

A)


B)

C)


D)

Question 16

Plot the point given in polar coordinates.

- $$\left( - 2,45 ^ { \circ } \right)$$

A)


B)

C)


D)

Question 17

Match the point in polar coordinates with either A, B, C, or D on the graph.

- $$\left( 3 , - \frac { 5 \pi } { 3 } \right)$$

A) A
B) B
C) C
D) D

Question 18

Plot the point given in polar coordinates.

- $$\left. ( 2,360 ) ^ { 0 } \right)$$

A)


B)

C)


D)

Question 19

Plot the point given in polar coordinates.

- $$\left( - 3 , - \frac { \pi } { 4 } \right)$$

A)


B)

C)

D)

Question 20

Plot the point given in polar coordinates.

- $\left(-4,405^{\circ}\right)$

A)


B)

C)


D)

Question 21

The polar coordinates of a point are given. Find the rectangular coordinates of the point.
(4, 70°) Round the rectangular coordinates to two decimal places.

A) (4.01, 1.59)
B) (1.37, 3.76)
C) (1.59, 4.01)
D) (3.76, 1.37)

Question 22

The polar coordinates of a point are given. Find the rectangular coordinates of the point.

- $\left( - 5 , \frac { 3 \pi } { 4 } \right)$

A) $\left( \frac { - 5 \sqrt { 2 } } { 2 } , \frac { - 5 \sqrt { 2 } } { 2 } \right)$
B) $\left( \frac { - 5 \sqrt { 2 } } { 2 } , \frac { 5 \sqrt { 2 } } { 2 } \right)$
C) $\left( \frac { 5 \sqrt { 2 } } { 2 } , \frac { - 5 \sqrt { 2 } } { 2 } \right)$
D) $\left( \frac { 5 \sqrt { 2 } } { 2 } , \frac { 5 \sqrt { 2 } } { 2 } \right)$

Question 23

The polar coordinates of a point are given. Find the rectangular coordinates of the point.

- $$\left( - 5 , - 360 ^ { \circ } \right)$$

A) $( 5,0 )$
B) $( - 5,0 )$
C) $( 0,5 )$
D) $( 0 , - 5 )$

Question 24

The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, θ).

- $$x ^ { 2 } + 4 y ^ { 2 } = 4$$

A) $4 \cos ^ { 2 } \theta + \sin ^ { 2 } \theta = 4 \mathrm { r }$
B) $\cos ^ { 2 } \theta + 4 \sin ^ { 2 } \theta = 4 \mathrm { r }$
C) $r ^ { 2 } \left( \cos ^ { 2 } \theta + 4 \sin ^ { 2 } \theta \right) = 4$
D) $\mathrm { r } ^ { 2 } \left( 4 \cos ^ { 2 } \theta + \sin ^ { 2 } \theta \right) = 4$

Question 25

The polar coordinates of a point are given. Find the rectangular coordinates of the point.

- $\left( 5 , - \frac { 4 \pi } { 3 } \right)$

A) $\left( \frac { 5 \sqrt { 3 } } { 2 } , \frac { 5 } { 2 } \right)$
B) $\left( - \frac { 5 } { 2 } , \frac { 5 \sqrt { 3 } } { 2 } \right)$
C) $\left( \frac { 5 } { 2 } , - \frac { 5 \sqrt { 3 } } { 2 } \right)$
D) $\left( - \frac { 5 \sqrt { 3 } } { 2 } , - \frac { 5 } { 2 } \right)$

Question 26

The rectangular coordinates of a point are given. Find polar coordinates for the point.

- $( - 7,0 )$

A) $\left( 7 , \frac { \pi } { 2 } \right)$
B) $\left( 7 , \frac { 3 \pi } { 2 } \right)$
C) $( 7 , \pi )$
D) $( - 7 , \pi )$

Question 27

The rectangular coordinates of a point are given. Find polar coordinates for the point.

- $( \sqrt { 3 } , - 1 )$

A) $\left( 2 , - \frac { \pi } { 6 } \right)$
B) $\left( 2 , \frac { 5 \pi } { 6 } \right)$
C) $\left( 2 , \frac { \pi } { 6 } \right)$
D) $\left( 2 , - \frac { 5 \pi } { 6 } \right)$

Question 28

The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, θ).

- $$y ^ { 2 } = 16 x$$

A) $r \sin ^ { 2 } \theta = 16 \cos \theta$
B) $\sin ^ { 2 } \theta = 16 \mathrm { r } \cos \theta$
C) $r ^ { 2 } \sin ^ { 2 } \theta = 16 \cos \theta$
D) $\sin ^ { 2 } \theta = 16 r ^ { 2 } \cos \theta$

Question 29

The polar coordinates of a point are given. Find the rectangular coordinates of the point.

- $\left( 5 , \frac { 3 \pi } { 4 } \right)$

A) $\left( \frac { - 5 \sqrt { 2 } } { 2 } , \frac { 5 \sqrt { 2 } } { 2 } \right)$
B) $\left( \frac { - 5 \sqrt { 2 } } { 2 } , \frac { - 5 \sqrt { 2 } } { 2 } \right)$
C) $\left( \frac { 5 \sqrt { 2 } } { 2 } , \frac { - 5 \sqrt { 2 } } { 2 } \right)$
D) $\left( \frac { 5 \sqrt { 2 } } { 2 } , \frac { 5 \sqrt { 2 } } { 2 } \right)$

Question 30

The rectangular coordinates of a point are given. Find polar coordinates for the point.
(-2, 0.6) Round the polar coordinates to two decimal places, with θ in radians.

A) (-2.09, 1.28)
B) (2.09, -1.28)
C) (2.09, 1.28)
D) (2.09, 2.85)

Question 31

The rectangular coordinates of a point are given. Find polar coordinates for the point.

-(0, 9)

A) $( 9,0 )$
B) $\left( 9 , - \frac { \pi } { 2 } \right)$
C) $( 9 , \pi )$
D) $\left( 9 , \frac { \pi } { 2 } \right)$

Question 32

The rectangular coordinates of a point are given. Find polar coordinates for the point.
(0.6, -1.1) Round the polar coordinates to two decimal places, with θ in degrees.

A) (1.25, -61.39°)
B) (1.25, 57.93°)
C) (1.25, -57.93°)
D) (1.25, 61.39°)

Question 33

The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, θ).

- $$x ^ { 2 } + y ^ { 2 } - 4 x = 0$$

A) $r = 4 \cos \theta$
B) $r \cos ^ { 2 } \theta = 4 \sin \theta$
C) $r \sin ^ { 2 } \theta = 4 \cos \theta$
D) $r = 4 \sin \theta$

Question 34

The polar coordinates of a point are given. Find the rectangular coordinates of the point.

- $\left( - 9 , \frac { 2 \pi } { 3 } \right)$

A) $\left( \frac { 9 } { 2 } , \frac { 9 \sqrt { 3 } } { 2 } \right)$
B) $\left( - \frac { 9 } { 2 } , \frac { 9 \sqrt { 3 } } { 2 } \right)$
C) $\left( \frac { 9 } { 2 } , \frac { - 9 \sqrt { 3 } } { 2 } \right)$
D) $\left( - \frac { 9 } { 2 } , \frac { - 9 \sqrt { 3 } } { 2 } \right)$

Question 35

The rectangular coordinates of a point are given. Find polar coordinates for the point.

-(-3, 3)

A) $\left( 3 \sqrt { 2 } , - \frac { 3 \pi } { 4 } \right)$
B) $\left( - 3 \sqrt { 2 } , - \frac { 3 \pi } { 4 } \right)$
C) $\left( - 3 \sqrt { 2 } , \frac { \pi } { 4 } \right)$
D) $\left( 3 \sqrt { 2 } , \frac { 3 \pi } { 4 } \right)$

Question 36

The polar coordinates of a point are given. Find the rectangular coordinates of the point.

- $\left( - 5,120 ^ { \circ } \right)$

A) $\left( - \frac { 5 } { 2 } , \frac { 5 \sqrt { 3 } } { 2 } \right)$
B) $\left( - \frac { 5 } { 2 } , \frac { - 5 \sqrt { 3 } } { 2 } \right)$
C) $\left( \frac { 5 } { 2 } , \frac { 5 \sqrt { 3 } } { 2 } \right)$
D) $\left( \frac { 5 } { 2 } , \frac { - 5 \sqrt { 3 } } { 2 } \right)$

Question 37

The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, θ).

- $$x ^ { 2 } = 4 y$$

A) $r \sin ^ { 2 } \theta = 4 \cos \theta$
B) $4 \sin ^ { 2 } \theta = r \cos \theta$
C) $4 \cos ^ { 2 } \theta = r \sin \theta$
D) $r \cos ^ { 2 } \theta = 4 \sin \theta$

Question 38

The polar coordinates of a point are given. Find the rectangular coordinates of the point.
(400, 130°) Round the rectangular coordinates to two decimal places.

A) (306.42, -257.12)
B) (-257.12, -306.42)
C) (-257.12, 306.42)
D) (306.42, 257.12)

Question 39

The polar coordinates of a point are given. Find the rectangular coordinates of the point.

- $$\left( - 3 , - 135 ^ { \circ } \right)$$

A) $\left( \frac { - 3 \sqrt { 2 } } { 2 } , \frac { - 3 \sqrt { 2 } } { 2 } \right)$
B) $\left( \frac { 3 \sqrt { 2 } } { 2 } , \frac { - 3 \sqrt { 2 } } { 2 } \right)$
C) $\left( \frac { 3 \sqrt { 2 } } { 2 } , \frac { 3 \sqrt { 2 } } { 2 } \right)$
D) $\left( \frac { - 3 \sqrt { 2 } } { 2 } , \frac { 3 \sqrt { 2 } } { 2 } \right)$

Question 40

The rectangular coordinates of a point are given. Find polar coordinates for the point.
(100, -30) Round the polar coordinates to two decimal places, with θ in degrees.

A) (104.40, 16.70°)
B) (104.40, -106.70°)
C) (104.40, -16.70°)
D) (104.40, 106.70°)

Question 41

Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation.

- $$r \sin \theta = 4$$

A)

$x = - 4$ ; vertical line 4 units
to the left of the pole

B)

$x = 4$ ; vertical line 4 units
to the right of the pole

C)

$y = - 4$ ; horizontal line 4 units
below the pole

D)

$y = 4$ ; horizontal line 4 units
above the pole

Question 42

Match the graph to one of the polar equations.

-

A) $r \sin \theta = 3$
B) $r = 6 \cos \theta$
C) $r = 6 \sin \theta$
D) $r = 3$

Question 43

Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation.

- $$r = 6 \sin \theta$$

A)

$x^{2}+(y-3)^{2}=9 ;$ circle, radius 3 center at $(0,3)$ in rectangular coordinates

B)

$$(x+3)^{2}+y^{2}=9 \text {; circle, radius 3 }$$
center at $(-3,0)$ in rectangular coordinates

C)

$(x-3)^{2}+y^{2}=9$ ; circle, radius 3 , center at $(3,0)$ in rectangular coordinates

D)

$\mathrm{x}^{2}+(\mathrm{y}+3)^{2}=9$ ; circle, radius 3 center at $(0,-3)$ in rectangular coordinates

Question 44

The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, θ).

- $$2 x + 3 y = 6$$

A) $2 \sin \theta + 3 \cos \theta = 6 r$
B) $2 \cos \theta + 3 \sin \theta = 6 r$
C) $\mathrm { r } ( 2 \cos \theta + 3 \sin \theta ) = 6$
D) $r ( 2 \sin \theta + 3 \cos \theta ) = 6$

Question 45

The letters r and θ represent polar coordinates. Write the equation using rectangular coordinates (x, y).

- $$r ( 1 - 2 \cos \theta ) = 1$$

A) $x ^ { 2 } + y ^ { 2 } = ( 1 + 2 x ) ^ { 2 }$
B) $x ^ { 2 } + y ^ { 2 } = 1 + 2 x$
C) $x ^ { 2 } + y ^ { 2 } = 2 + x$
D) $x ^ { 2 } + y ^ { 2 } = ( 2 + x ) ^ { 2 }$

Question 46

The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, θ).

- $$y = x$$

A) $r = \cos \theta$
B) $\sin \theta = \cos \theta$
C) $\sin \theta = - \cos \theta$
D) $r = \sin \theta$

Question 47

The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, θ).

- $$y = 5$$

A) $r = 5$
B) $r \cos \theta = 5$
C) $r \sin \theta = 5$
D) $\sin \theta \cos \theta = 5$

Question 48

Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation.

- $$r \sec \theta = - 6$$

A)

$( x + 3 ) ^ { 2 } + y ^ { 2 } = 9$ ; circle, radius 3
center $( - 3,0 )$ in rectangular coordinates

B)

$y = - 6$ ; horizontal line 6 units
below the pole

C)

$x = - 6$ ; vertical line 6 units
to the left of the pole

D)

$x ^ { 2 } + ( y + 3 ) ^ { 2 } = 9$ ; circle, radius 3
center at $( 0 , - 3 )$ in rectangular coordinates

Question 49

The letters r and θ represent polar coordinates. Write the equation using rectangular coordinates (x, y).

- $$r = \frac { 5 } { 1 + \cos \theta }$$

A) $x ^ { 2 } = 25 - 10 y$
B) $y ^ { 2 } = 25 - 10 x$
C) $x ^ { 2 } = 10 y - 25$
D) $\mathrm { y } ^ { 2 } = 10 \mathrm { x } - 25$

Question 50

The letters r and θ represent polar coordinates. Write the equation using rectangular coordinates (x, y).

- $$\mathrm { r } = 1 + 2 \sin \theta$$

A) $\sqrt { x ^ { 2 } + y ^ { 2 } } = x ^ { 2 } + y ^ { 2 } + 2 y$
B) $x ^ { 2 } + y ^ { 2 } = \sqrt { x ^ { 2 } + y ^ { 2 } } + 2 y$
C) $x ^ { 2 } + y ^ { 2 } = \sqrt { x ^ { 2 } + y ^ { 2 } } + 2 x$
D) $\sqrt { x ^ { 2 } + y ^ { 2 } } = x ^ { 2 } + y ^ { 2 } + 2 x$

Question 51

Match the graph to one of the polar equations.

-

A) $r = 2 \sin \theta$
B) $r = 2 \cos \theta$
C) $r \sin \theta = 1$
D) $r = 1$

Question 52

Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation.

- $r=6 \cos \theta$

A)

$(x-3)^{2}+y^{2}=9 ;$ circle, radius 3 center at $(3,0)$ in rectangular coordinates

B)

$x^{2}+(y+3)^{2}=9 ;$ circle, radius 3
center at $(0,-3)$ in rectangular coordinates

C)

$(x+3)^{2}+y^{2}=9$ ; circle, radius 3 ,
center at $(-3,0)$ in rectangular coordinates

D)


$\mathrm{x}^{2}+(\mathrm{y}-3)^{2}=9$ ; circle, radius 3 ,
center at $(0,3)$ in rectangular coordinates

Question 53

The letters r and θ represent polar coordinates. Write the equation using rectangular coordinates (x, y).

- $\mathrm { r } \sin \theta = 10$

A) $y = 10$
B) $x = 10$
C) $x = 10 y$
D) $y = 10 x$

Question 54

The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, θ).

- $$x y = 1$$

A) $r \sin 2 \theta = 2$
B) $r ^ { 2 } \sin 2 \theta = 2$
C) $2 r ^ { 2 } \sin \theta \cos \theta = 1$
D) $2 r \sin \theta \cos \theta = 1$

Question 55

The letters r and θ represent polar coordinates. Write the equation using rectangular coordinates (x, y).

- $$\mathrm { r } = 2 ( \sin \theta - \cos \theta )$$

A) $x ^ { 2 } + y ^ { 2 } = 2 y - 2 x$
B) $x ^ { 2 } + y ^ { 2 } = 2 x - 2 y$
C) $2 x ^ { 2 } + 2 y ^ { 2 } = y - x$
D) $2 x ^ { 2 } + 2 y ^ { 2 } = x - y$

Question 56

The letters r and θ represent polar coordinates. Write the equation using rectangular coordinates (x, y).

- $$r = 5$$

A) $x + y = 5$
B) $x ^ { 2 } - y ^ { 2 } = 25$
C) $x ^ { 2 } + y ^ { 2 } = 25$
D) $x + y = 25$

Question 57

The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, θ).

- $$x = - 3$$

A) $r \cos \theta = - 3$
B) $\mathbf { r } \cos \theta = 3$
C) $r \sin \theta = - 3$
D) $r \sin \theta = 3$

Question 58

Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation.

- $$\theta = \frac { \pi } { 3 }$$

A)

$y=\sqrt{3} x$ ; line through the pole making
an angle of $\frac{\pi}{3}$ with the polar axis

B)

$y=-\frac{\sqrt{3}}{3} x$ ; line through the pole making
an angle of $\frac{\pi}{3}$ with the polar axis

C)

$y=-\frac{\pi}{3}$ ; horizontal line $\frac{\pi}{3}$ units
below the pole

D)

$\left(x-\frac{\pi}{3}\right)^{2}+y^{2}=\frac{\pi^{2}}{9} ;$ circle, radius $\frac{\pi}{3}$
center at $\left(\frac{\pi}{3}, 0\right)$ in rectangular coordinates

Question 59

The letters r and θ represent polar coordinates. Write the equation using rectangular coordinates (x, y).

- $$r = \cos \theta$$

A) $x ^ { 2 } + y ^ { 2 } = x$
B) $x ^ { 2 } + y ^ { 2 } = y$
C) $( x + y ) ^ { 2 } = y$
D) $( x + y ) ^ { 2 } = x$

Question 60

The letters r and θ represent polar coordinates. Write the equation using rectangular coordinates (x, y).

- $r = 10 \sin \theta$

A) $\sqrt { x ^ { 2 } + y ^ { 2 } } = 10 y$
B) $\sqrt { x ^ { 2 } + y ^ { 2 } } = 10 x$
C) $x ^ { 2 } + y ^ { 2 } = 10 x$
D) $x ^ { 2 } + y ^ { 2 } = 10 y$

Question 61

Identify and graph the polar equation.

- $r=3-4 \sin \theta$

A)
11e81ee_3c59_064b_a8e7_911a803408be_TB7697_11
limacon without inner loop

B)

limacon with inner loop
C)

limacon with inner loop

D)

limacon without inner loop

Question 62

Test the equation for symmetry with respect to the given axis, line, or pole.

- $$r = 4 - 4 \sin \theta ; \text { polar axis }$$

A) Symmetric with respect to the polar axis
B) May or may not be symmetric with respect to the polar axis

Question 63

Match the graph to one of the polar equations.

-

A) $r = 2 \sin \theta$
B) $r = 2 \cos \theta$
C) $r = 1$
D) $r \sin \theta = 1$

Question 64

Test the equation for symmetry with respect to the given axis, line, or pole.

- $r = 3 \sin ( 3 \theta ) ;$ the line $\theta = \frac { \pi } { 2 }$

A) Symmetric with respect to the line $\theta = \frac { \pi } { 2 }$
B) May or may not be symmetric with respect to the line $\theta = \frac { \pi } { 2 }$

Question 65

Identify and graph the polar equation.

- $r=4 \sin (2 \theta)$

A)

circle

B)

rose with four petals
C)

rose with two petals

D)

lemniscate

Question 66

Test the equation for symmetry with respect to the given axis, line, or pole.

- $$r = 3 - 6 \sin \theta \text {; the polar axis }$$

A) May or may not be symmetric with respect to the polar axis
B) Symmetric with respect to the polar axis

Question 67

Test the equation for symmetry with respect to the given axis, line, or pole.

- $r = 3 + 3 \cos \theta ;$ the line $\theta = \frac { \pi } { 2 }$

A) Symmetric with respect to the line $\theta = \frac { \pi } { 2 }$
B) May or may not be symmetric with respect to the line $\theta = \frac { \pi } { 2 }$

Question 68

Test the equation for symmetry with respect to the given axis, line, or pole.

- $\mathrm { r } = - 4 \cos \theta$ ; the polar axis

A) May or may not be symmetric with respect to the polar axis
B) Symmetric with respect to the polar axis

Question 69

Identify and graph the polar equation.

- $r^{2}=4 \cos (2 \theta)$

A)

rose with four petals
B)

lemniscate
C)

lemniscate

D)

rose with four petals

Question 70

Identify and graph the polar equation.

- $r=5-4 \cos \theta$

A)

limacon without inner loop

B)

limacon without inner loop
C)

limacon with inner loop


D)

limacon with inner loop

Question 71

Test the equation for symmetry with respect to the given axis, line, or pole.

- $$\mathrm { r } ^ { 2 } = \sin ( 2 \theta ) \text {; the pole }$$

A) Symmetric with respect to the pole
B) May or may not be symmetric with respect to the pole

Question 72

Test the equation for symmetry with respect to the given axis, line, or pole.

- $$r = 6 + 2 \cos \theta ; \text { the pole }$$

A) Symmetric with respect to the pole
B) May or may not be symmetric with respect to the pole

Question 73

Identify and graph the polar equation.

- $r=1-\cos \theta$

A)

cardioid

B)

cardioid
C)

cardioid

D)

cardioid

Question 74

Test the equation for symmetry with respect to the given axis, line, or pole.

- $r = 2 \sin \theta$ ; the pole

A) Symmetric with respect to the pole
B) May or may not be symmetric with respect to the pole

Question 75

Match the graph to one of the polar equations.

-

A) $r = 3 + \sin \theta$
B) $r = 6 \sin \theta$
C) $r = 3 + \cos \theta$
D) $r = 6 \cos \theta$

Question 76

Test the equation for symmetry with respect to the given axis, line, or pole.

- $r = 4 \cos \theta ;$ the line $\theta = \frac { \pi } { 2 }$

A) May or may not be symmetric with respect to the line $\theta = \frac { \pi } { 2 }$
B) Symmetric with respect to the line $\theta = \frac { \pi } { 2 }$

Question 77

Match the graph to one of the polar equations.

-

A) $r = 3 + \sin \theta$
B) $r = 3 + \cos \theta$
C) $r = 6 \cos \theta$
D) $r = 6 \sin \theta$

Question 78

Identify and graph the polar equation.

- $$r = 4 \theta$$

A)

logarithmic spiral
B)

logarithmic spiral
C)

logarithmic spiral

D)


logarithmic spiral

Question 79

Match the graph to one of the polar equations.

-

A) $r = - 2 \cos \theta$
B) $r \sin \theta = - 1$
C) $r = - 2 \sin \theta$
D) $r = - 1$

Question 80

Test the equation for symmetry with respect to the given axis, line, or pole.

- $r = 6 + 2 \sin \theta ;$ the line $\theta = \frac { \pi } { 2 }$

A) May or may not be symmetric with respect to the line $\theta = \frac { \pi } { 2 }$
B) Symmetric with respect to the line $\theta = \frac { \pi } { 2 }$