Question 1

Convert the polar equation to rectangular form.​ $r = 4 \csc \theta$ ​

Accepted Answer

A)  $y = 4$ 
B)  $y = 4 \mathrm { r }$ 
C)  $x = 4$ 
D)  $6 y = \mathrm { r }$ 
E)  $x = 4 \mathrm { r }$ 
A)  $y = 4$ 
B)  $y = 4 \mathrm { r }$ 
C)  $x = 4$ 
D)  $6 y = \mathrm { r }$ 
E)  $x = 4 \mathrm { r }$

Question 2

Describe the graph of the polar equation and find the corresponding rectangular equation.Select the correct graph.​ $$r = 2 \sec \theta$$ ​

Accepted Answer

A) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​ $$x - 5 = 0$$ ​   
B) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​ $$x - 2 = 0$$ ​   
C) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​ $$x + 2 = 0$$ ​   
D) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​ $$x - 3 = 0$$ ​
​   
E) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​ $$x - 3 = 0$$ ​   
A) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​ $$x - 5 = 0$$ ​   
B) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​ $$x - 2 = 0$$ ​   
C) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​ $$x + 2 = 0$$ ​   
D) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​ $$x - 3 = 0$$ ​
​   
E) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​ $$x - 3 = 0$$ ​

Question 3

A point in polar coordinates is given.Convert the point to rectangular coordinates.Round your answers to one decimal places.​ $$( - 2.1,1.1 )$$ ​

Accepted Answer

A) Rectangular coordinates: (1.9,1.0) 
B) Rectangular coordinates: (-1.0,-1.9) 
C) Rectangular coordinates: (2.1,1.1) 
D) Rectangular coordinates: (-1.9,-1.0) 
E) Rectangular coordinates: (1.0,1.9) 
A) Rectangular coordinates: (1.9,1.0) 
B) Rectangular coordinates: (-1.0,-1.9) 
C) Rectangular coordinates: (2.1,1.1) 
D) Rectangular coordinates: (-1.9,-1.0) 
E) Rectangular coordinates: (1.0,1.9)

Question 4

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places.​ $$( 3.5,1.62 )$$ ​

Accepted Answer

A) Rectangular coordinates: (3.5,1.62) 
B) Rectangular coordinates: (4.50,0.83) 
C) Rectangular coordinates: (-0.17,3.50) 
D) Rectangular coordinates: (0.83,4.50) 
E) Rectangular coordinates: (3.50,-0.17) 
A) Rectangular coordinates: (3.5,1.62) 
B) Rectangular coordinates: (4.50,0.83) 
C) Rectangular coordinates: (-0.17,3.50) 
D) Rectangular coordinates: (0.83,4.50) 
E) Rectangular coordinates: (3.50,-0.17)

Question 5

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places.​ $$( 8.98,3.0 )$$ ​

Accepted Answer

A) Rectangular coordinates: (2.27,-7.89) 
B) Rectangular coordinates: (-7.89,2.27) 
C) Rectangular coordinates: (1.27,-8.89) 
D) Rectangular coordinates: (-8.89,1.27) 
E) Rectangular coordinates: (8.98,4.50) 
A) Rectangular coordinates: (2.27,-7.89) 
B) Rectangular coordinates: (-7.89,2.27) 
C) Rectangular coordinates: (1.27,-8.89) 
D) Rectangular coordinates: (-8.89,1.27) 
E) Rectangular coordinates: (8.98,4.50)

Question 6

Convert the polar equation to rectangular form.​ $r = 2 \sin \theta$ ​

Accepted Answer

A)  $x ^ { 2 } + y ^ { 2 } - 2 y = 0$ 
B)  $x ^ { 2 } + y ^ { 2 } + 2 y = 0$ 
C)  $x ^ { 2 } + y ^ { 2 } - 2 \mathrm { x } = 0$ 
D)  $x ^ { 2 } + y ^ { 2 } + 2 \mathrm { x } = 0$ 
E)  $x ^ { 2 } + y ^ { 2 } - 2 = 0$ 
A)  $x ^ { 2 } + y ^ { 2 } - 2 y = 0$ 
B)  $x ^ { 2 } + y ^ { 2 } + 2 y = 0$ 
C)  $x ^ { 2 } + y ^ { 2 } - 2 \mathrm { x } = 0$ 
D)  $x ^ { 2 } + y ^ { 2 } + 2 \mathrm { x } = 0$ 
E)  $x ^ { 2 } + y ^ { 2 } - 2 = 0$

Question 7

Convert the polar equation to rectangular form.​ $r = 6 \cos 2 \theta$ ​

Accepted Answer

A)  $\left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } = 36 \left( x ^ { 2 } - y ^ { 2 } \right) ^ { 2 }$ 
B)  $\left( x ^ { 2 } + y ^ { 2 } \right) ^ { 3 } = 6 \left( x ^ { 2 } - y ^ { 2 } \right) ^ { 3 }$ 
C)  $\left( x ^ { 2 } + y ^ { 2 } \right) ^ { 3 } = 36 \left( x ^ { 2 } - y ^ { 2 } \right) ^ { 3 }$ 
D)  $\left( x ^ { 2 } + y ^ { 2 } \right) ^ { 3 } = 6 \left( x ^ { 2 } - y ^ { 2 } \right) ^ { 2 }$ 
E)  $\left( x ^ { 2 } + y ^ { 2 } \right) ^ { 3 } = 36 \left( x ^ { 2 } - y ^ { 2 } \right) ^ { 2 }$ 
A)  $\left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } = 36 \left( x ^ { 2 } - y ^ { 2 } \right) ^ { 2 }$ 
B)  $\left( x ^ { 2 } + y ^ { 2 } \right) ^ { 3 } = 6 \left( x ^ { 2 } - y ^ { 2 } \right) ^ { 3 }$ 
C)  $\left( x ^ { 2 } + y ^ { 2 } \right) ^ { 3 } = 36 \left( x ^ { 2 } - y ^ { 2 } \right) ^ { 3 }$ 
D)  $\left( x ^ { 2 } + y ^ { 2 } \right) ^ { 3 } = 6 \left( x ^ { 2 } - y ^ { 2 } \right) ^ { 2 }$ 
E)  $\left( x ^ { 2 } + y ^ { 2 } \right) ^ { 3 } = 36 \left( x ^ { 2 } - y ^ { 2 } \right) ^ { 2 }$

Question 8

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places.​ $$\left( 8 , \frac { 7 \pi } { 5 } \right)$$ ​

Accepted Answer

A) Rectangular coordinates: (7.61,0.07) 
B) Rectangular coordinates: (7.61,-7.61) 
C) Rectangular coordinates: (-2.47,-7.61) 
D) Rectangular coordinates: (-2.47,7.61) 
E) Rectangular coordinates: (-2.47,0.07) 
A) Rectangular coordinates: (7.61,0.07) 
B) Rectangular coordinates: (7.61,-7.61) 
C) Rectangular coordinates: (-2.47,-7.61) 
D) Rectangular coordinates: (-2.47,7.61) 
E) Rectangular coordinates: (-2.47,0.07)

Question 9

Convert the rectangular equation to polar form.Assume r > 1.​ $x ^ { 2 } + y ^ { 2 } = 49$ ​

Accepted Answer

A)  $r = 7$ 
B)  $r = - 7$ 
C)  $r = \frac { 1 } { 7 }$ 
D)  $r = 49$ 
E)  $r = - \frac { 1 } { 7 }$ 
A)  $r = 7$ 
B)  $r = - 7$ 
C)  $r = \frac { 1 } { 7 }$ 
D)  $r = 49$ 
E)  $r = - \frac { 1 } { 7 }$

Question 10

A point (a,b)shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates.​   ​ $$a = 3 , b = \frac { 3 \pi } { 2 }$$ ​

Accepted Answer

A) Rectangular coordinates: (0,3) 
B) Rectangular coordinates: (-3,0) 
C) Rectangular coordinates: (3,0) 
D) Rectangular coordinates: (0,-3) 
E) Rectangular coordinates: (3,3) 
A) Rectangular coordinates: (0,3) 
B) Rectangular coordinates: (-3,0) 
C) Rectangular coordinates: (3,0) 
D) Rectangular coordinates: (0,-3) 
E) Rectangular coordinates: (3,3)

Question 11

A point in rectangular coordinates is given.Convert the point to polar coordinates,r > 0.​ $$( - 7,7 )$$ ​

Accepted Answer

A) Polar coordinates: $\left( - \sqrt { 7 } , \frac { \pi } { 4 } \right)$ 
B) Polar coordinates: $\left( \sqrt { 98 } , \frac { 3 \pi } { 4 } \right)$ 
C) Polar coordinates: $\left( \sqrt { 98 } , - \frac { 3 \pi } { 4 } \right)$ 
D) Polar coordinates: $\left( - \sqrt { 98 } , \frac { 3 \pi } { 4 } \right)$ 
E) Polar coordinates: $\left( \sqrt { 7 } , \frac { \pi } { 4 } \right)$ 
A) Polar coordinates: $\left( - \sqrt { 7 } , \frac { \pi } { 4 } \right)$ 
B) Polar coordinates: $\left( \sqrt { 98 } , \frac { 3 \pi } { 4 } \right)$ 
C) Polar coordinates: $\left( \sqrt { 98 } , - \frac { 3 \pi } { 4 } \right)$ 
D) Polar coordinates: $\left( - \sqrt { 98 } , \frac { 3 \pi } { 4 } \right)$ 
E) Polar coordinates: $\left( \sqrt { 7 } , \frac { \pi } { 4 } \right)$

Question 12

Convert the rectangular equation to polar form.Assume a > 0,r > 1.​ $x ^ { 2 } + y ^ { 2 } = 4 a ^ { 2 }$ ​

Accepted Answer

A)  $r = 2 a$ 
B)  $r = - 42 a$ 
C)  $r = 2$ 
D)  $r = - 2 a ^ { 2 }$ 
E)  $r = 2 a ^ { 2 }$ 
A)  $r = 2 a$ 
B)  $r = - 42 a$ 
C)  $r = 2$ 
D)  $r = - 2 a ^ { 2 }$ 
E)  $r = 2 a ^ { 2 }$

Question 13

Convert the rectangular equation to polar form.Assume r > 1.​ $x = 17 a$ ​

Accepted Answer

A)  $r = \operatorname { acsc } \theta$ 
B)  $r = 17 \mathrm { a } \cos \theta$ 
C)  $r = 17 \sin \theta$ 
D)  $r = 17 \operatorname { acsc } \theta$ 
E)  $r = 17 \text { asec } \theta$ 
A)  $r = \operatorname { acsc } \theta$ 
B)  $r = 17 \mathrm { a } \cos \theta$ 
C)  $r = 17 \sin \theta$ 
D)  $r = 17 \operatorname { acsc } \theta$ 
E)  $r = 17 \text { asec } \theta$

Question 14

Convert the rectangular equation to polar form.Assume r > 1.​ $y = 2$ ​

Accepted Answer

A)  $r = 2 \cos \theta$ 
B)  $r = \csc \theta$ 
C)  $r = 2 \csc \theta$ 
D)  $r = 2 \sin \theta$ 
E)  $r = 2 \sec \theta$ 
A)  $r = 2 \cos \theta$ 
B)  $r = \csc \theta$ 
C)  $r = 2 \csc \theta$ 
D)  $r = 2 \sin \theta$ 
E)  $r = 2 \sec \theta$

Question 15

Convert the rectangular equation to polar form.Assume r > 1.​ $y = 6$ ​

Accepted Answer

A)  $r = 6 \csc \theta$ 
B)  $r = 6 \cos \theta$ 
C)  $r = 6 \cot \theta$ 
D)  $r = 6 \sin \theta$ 
E)  $r = 6 \sec \theta$ 
A)  $r = 6 \csc \theta$ 
B)  $r = 6 \cos \theta$ 
C)  $r = 6 \cot \theta$ 
D)  $r = 6 \sin \theta$ 
E)  $r = 6 \sec \theta$

Question 16

A point in polar coordinates is given.Convert the point to rectangular coordinates.Round your answers to one decimal places.​ $$( - 6,3.56 )$$ ​

Accepted Answer

A) Rectangular coordinates: (3.6,6.0) 
B) Rectangular coordinates: (5.5,2.4) 
C) Rectangular coordinates: (-5.5,-2.4) 
D) Rectangular coordinates: (-2.4,-5.5) 
E) Rectangular coordinates: (2.4,5.5) 
A) Rectangular coordinates: (3.6,6.0) 
B) Rectangular coordinates: (5.5,2.4) 
C) Rectangular coordinates: (-5.5,-2.4) 
D) Rectangular coordinates: (-2.4,-5.5) 
E) Rectangular coordinates: (2.4,5.5)

Question 17

A point in rectangular coordinates is given.Convert the point to polar coordinates,r > 0.​ $( - \sqrt { 19 } , \sqrt { 19 } )$ ​

Accepted Answer

A) Polar coordinates: $\left( \sqrt { 38 } , \frac { 3 \pi } { 4 } \right)$ 
B) Polar coordinates: $\left( \sqrt { 38 } , - \frac { \pi } { 4 } \right)$ 
C) Polar coordinates: $\left( \sqrt { 38 } , - \frac { 3 \pi } { 4 } \right)$ 
D) Polar coordinates: $\left( \sqrt { 38 } , \frac { \pi } { 4 } \right)$ 
E) Polar coordinates: $\left( \sqrt { 38 } , \frac { 5 \pi } { 4 } \right)$ 
A) Polar coordinates: $\left( \sqrt { 38 } , \frac { 3 \pi } { 4 } \right)$ 
B) Polar coordinates: $\left( \sqrt { 38 } , - \frac { \pi } { 4 } \right)$ 
C) Polar coordinates: $\left( \sqrt { 38 } , - \frac { 3 \pi } { 4 } \right)$ 
D) Polar coordinates: $\left( \sqrt { 38 } , \frac { \pi } { 4 } \right)$ 
E) Polar coordinates: $\left( \sqrt { 38 } , \frac { 5 \pi } { 4 } \right)$

Question 18

Convert the polar equation to rectangular form.​ $r = - 9 \sec \theta$ ​

Accepted Answer

A)  $y = - 9$ 
B)  $9 x = r$ 
C)  $x = 9$ 
D)  $y = 9$ 
E)  $x = - 9$ 
A)  $y = - 9$ 
B)  $9 x = r$ 
C)  $x = 9$ 
D)  $y = 9$ 
E)  $x = - 9$

Question 19

Convert the rectangular equation to polar form.Assume r > 1.​ $\left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } = 9 \left( x ^ { 2 } - y ^ { 2 } \right)$ ​

Accepted Answer

A)  $r ^ { 2 } = 9 \cos 2 \theta$ 
B)  $r ^ { 2 } = 9 \csc 2 \theta$ 
C)  $r ^ { 2 } = 9 \cos \theta$ 
D)  $r ^ { 2 } = 9 \sin 2 \theta$ 
E)  $r ^ { 2 } = 9 \sin \theta$ 
A)  $r ^ { 2 } = 9 \cos 2 \theta$ 
B)  $r ^ { 2 } = 9 \csc 2 \theta$ 
C)  $r ^ { 2 } = 9 \cos \theta$ 
D)  $r ^ { 2 } = 9 \sin 2 \theta$ 
E)  $r ^ { 2 } = 9 \sin \theta$

Question 20

Describe the graph of the polar equation and find the corresponding rectangular equation.Select the correct graph.​ $r = 2$ ​

Accepted Answer

A) The graph of the polar equation consists of all points that are two units from the pole. $x ^ { 2 } + y ^ { 2 } = - 4$   
B) The graph of the polar equation consists of all points that are two units from the pole. $$x ^ { 2 } + y ^ { 2 } = 4$$   
C) The graph of the polar equation consists of all points that are two units from the pole. $$x ^ { 2 } + y ^ { 2 } = 2$$   
D) The graph of the polar equation consists of all points that are two units from the pole. $$x ^ { 2 } + y ^ { 2 } = 4$$   
E) The graph of the polar equation consists of all points that are two units from the pole. $$x ^ { 2 } + y ^ { 2 } = 2$$   
A) The graph of the polar equation consists of all points that are two units from the pole. $x ^ { 2 } + y ^ { 2 } = - 4$   
B) The graph of the polar equation consists of all points that are two units from the pole. $$x ^ { 2 } + y ^ { 2 } = 4$$   
C) The graph of the polar equation consists of all points that are two units from the pole. $$x ^ { 2 } + y ^ { 2 } = 2$$   
D) The graph of the polar equation consists of all points that are two units from the pole. $$x ^ { 2 } + y ^ { 2 } = 4$$   
E) The graph of the polar equation consists of all points that are two units from the pole. $$x ^ { 2 } + y ^ { 2 } = 2$$

Exam 65: Polar Coordinates

Convert the polar equation to rectangular form.​ r=4csc⁡θr = 4 \csc \thetar=4cscθ ​

Describe the graph of the polar equation and find the corresponding rectangular equation.Select the correct graph.​ r=2sec⁡θr = 2 \sec \thetar=2secθ ​

A point in polar coordinates is given.Convert the point to rectangular coordinates.Round your answers to one decimal places.​ (−2.1,1.1)( - 2.1,1.1 )(−2.1,1.1) ​

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places.​ (3.5,1.62)( 3.5,1.62 )(3.5,1.62) ​

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places.​ (8.98,3.0)( 8.98,3.0 )(8.98,3.0) ​

Convert the polar equation to rectangular form.​ r=2sin⁡θr = 2 \sin \thetar=2sinθ ​

Convert the polar equation to rectangular form.​ r=6cos⁡2θr = 6 \cos 2 \thetar=6cos2θ ​

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places.​ (8,7π5)\left( 8 , \frac { 7 \pi } { 5 } \right)(8,57π​) ​

Convert the rectangular equation to polar form.Assume r > 1.​ x2+y2=49x ^ { 2 } + y ^ { 2 } = 49x2+y2=49 ​

A point (a,b)shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates.​ ​ a=3,b=3π2a = 3 , b = \frac { 3 \pi } { 2 }a=3,b=23π​ ​

A point in rectangular coordinates is given.Convert the point to polar coordinates,r > 0.​ (−7,7)( - 7,7 )(−7,7) ​

Convert the rectangular equation to polar form.Assume a > 0,r > 1.​ x2+y2=4a2x ^ { 2 } + y ^ { 2 } = 4 a ^ { 2 }x2+y2=4a2 ​

Convert the rectangular equation to polar form.Assume r > 1.​ x=17ax = 17 ax=17a ​

Convert the rectangular equation to polar form.Assume r > 1.​ y=2y = 2y=2 ​

Convert the rectangular equation to polar form.Assume r > 1.​ y=6y = 6y=6 ​

A point in polar coordinates is given.Convert the point to rectangular coordinates.Round your answers to one decimal places.​ (−6,3.56)( - 6,3.56 )(−6,3.56) ​

A point in rectangular coordinates is given.Convert the point to polar coordinates,r > 0.​ (−19,19)( - \sqrt { 19 } , \sqrt { 19 } )(−19​,19​) ​

Convert the polar equation to rectangular form.​ r=−9sec⁡θr = - 9 \sec \thetar=−9secθ ​

Convert the rectangular equation to polar form.Assume r > 1.​ (x2+y2)2=9(x2−y2)\left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } = 9 \left( x ^ { 2 } - y ^ { 2 } \right)(x2+y2)2=9(x2−y2) ​

Describe the graph of the polar equation and find the corresponding rectangular equation.Select the correct graph.​ r=2r = 2r=2 ​

Rectangular Coordinates

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Convert the polar equation to rectangular form. $r = 4 \csc \theta$

Describe the graph of the polar equation and find the corresponding rectangular equation.Select the correct graph. $r = 2 \sec \theta$

A point in polar coordinates is given.Convert the point to rectangular coordinates.Round your answers to one decimal places. $( - 2.1,1.1 )$

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places. $( 3.5,1.62 )$

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places. $( 8.98,3.0 )$

Convert the polar equation to rectangular form. $r = 2 \sin \theta$

Convert the polar equation to rectangular form. $r = 6 \cos 2 \theta$

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places. $\left( 8 , \frac { 7 \pi } { 5 } \right)$

Convert the rectangular equation to polar form.Assume r > 1. $x ^ { 2 } + y ^ { 2 } = 49$

A point (a,b)shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates. $A point (a,b)shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates. a = 3 , b = \frac { 3 \pi } { 2 } $ $a = 3 , b = \frac { 3 \pi } { 2 }$

A point in rectangular coordinates is given.Convert the point to polar coordinates,r > 0. $( - 7,7 )$

Convert the rectangular equation to polar form.Assume a > 0,r > 1. $x ^ { 2 } + y ^ { 2 } = 4 a ^ { 2 }$

Convert the rectangular equation to polar form.Assume r > 1. $x = 17 a$

Convert the rectangular equation to polar form.Assume r > 1. $y = 2$

Convert the rectangular equation to polar form.Assume r > 1. $y = 6$

A point in polar coordinates is given.Convert the point to rectangular coordinates.Round your answers to one decimal places. $( - 6,3.56 )$

A point in rectangular coordinates is given.Convert the point to polar coordinates,r > 0. $( - \sqrt { 19 } , \sqrt { 19 } )$

Convert the polar equation to rectangular form. $r = - 9 \sec \theta$

Convert the rectangular equation to polar form.Assume r > 1. $\left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } = 9 \left( x ^ { 2 } - y ^ { 2 } \right)$

Describe the graph of the polar equation and find the corresponding rectangular equation.Select the correct graph. $r = 2$