Question 1

Convert the rectangular equation to polar form.Assume r > 1.​ $7 x - y + 6 = 0$ ​

Accepted Answer

A)  $y = \frac { - 6 } { 7 \cos \Theta - 6 \sin \theta }$ 
B)  $y = \frac { - 7 } { 6 \cos \Theta - \sin \Theta }$ 
C)  $y = \frac { - 6 } { 7 \cos \theta + \sin \theta }$ 
D)  $y = \frac { 6 } { 7 \cos \theta - \sin \theta }$ 
E)  $y = \frac { - 6 } { 7 \cos \theta - \sin \theta }$ 
A)  $y = \frac { - 6 } { 7 \cos \Theta - 6 \sin \theta }$ 
B)  $y = \frac { - 7 } { 6 \cos \Theta - \sin \Theta }$ 
C)  $y = \frac { - 6 } { 7 \cos \theta + \sin \theta }$ 
D)  $y = \frac { 6 } { 7 \cos \theta - \sin \theta }$ 
E)  $y = \frac { - 6 } { 7 \cos \theta - \sin \theta }$ E

Question 2

Use a graphing utility to find one set of polar coordinates for the point given in rectangular coordinates,r > 0.Round your answers to three decimal places.​ $( 3 , - 2 )$ ​

Accepted Answer

A) Polar coordinates: $( \sqrt { 2 } , - 0.588 )$ 
B) Polar coordinates: $( \sqrt { 1 } , - 0.588 )$ 
C) Polar coordinates: $( \sqrt { 13 } , - 0.588 )$ 
D) Polar coordinates: $( \sqrt { 13 } , 0.588 )$ 
E) Polar coordinates: $( \sqrt { 3 } , - 0.588 )$ 
A) Polar coordinates: $( \sqrt { 2 } , - 0.588 )$ 
B) Polar coordinates: $( \sqrt { 1 } , - 0.588 )$ 
C) Polar coordinates: $( \sqrt { 13 } , - 0.588 )$ 
D) Polar coordinates: $( \sqrt { 13 } , 0.588 )$ 
E) Polar coordinates: $( \sqrt { 3 } , - 0.588 )$ C

Question 3

A point in rectangular coordinates is given.Convert the point to polar coordinates,r > 0.​ $( 0,4 )$ ​

Accepted Answer

A) Polar coordinates: $\left( 4 , - \frac { \pi } { 2 } \right)$ 
B) Polar coordinates: $\left( - 4 , - \frac { \pi } { 2 } \right)$ 
C) Polar coordinates: $\left( 4 , \frac { \pi } { 2 } \right)$ 
D) Polar coordinates: $\left( - 4 , \frac { 3 \pi } { 2 } \right)$ 
E) Polar coordinates: $\left( 4 , \frac { 3 \pi } { 2 } \right)$ 
A) Polar coordinates: $\left( 4 , - \frac { \pi } { 2 } \right)$ 
B) Polar coordinates: $\left( - 4 , - \frac { \pi } { 2 } \right)$ 
C) Polar coordinates: $\left( 4 , \frac { \pi } { 2 } \right)$ 
D) Polar coordinates: $\left( - 4 , \frac { 3 \pi } { 2 } \right)$ 
E) Polar coordinates: $\left( 4 , \frac { 3 \pi } { 2 } \right)$ C

Question 4

Convert the rectangular equation to polar form.Assume a > 0,r > 1.​ $x ^ { 2 } + y ^ { 2 } - 3 a y = 0$ ​

Accepted Answer

A)  $r = 3 a \sin \theta$ 
B)  $r = 3 a \cot \Theta$ 
C)  $r = 3 a \cos \theta$ 
D)  $r = 3 \operatorname { asec } \theta$ 
E)  $r = 3 \operatorname { acsc } \theta$ 
A)  $r = 3 a \sin \theta$ 
B)  $r = 3 a \cot \Theta$ 
C)  $r = 3 a \cos \theta$ 
D)  $r = 3 \operatorname { asec } \theta$ 
E)  $r = 3 \operatorname { acsc } \theta$

Question 5

A point (a,b)shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates.​   ​ $$a = 6 , b = \frac { \pi } { 2 }$$ ​

Accepted Answer

A) Rectangular coordinates: (6,6) 
B) Rectangular coordinates: (6,0) 
C) Rectangular coordinates: (0,6) 
D) Rectangular coordinates: (-6,0) 
E) Rectangular coordinates: (0,-6) 
A) Rectangular coordinates: (6,6) 
B) Rectangular coordinates: (6,0) 
C) Rectangular coordinates: (0,6) 
D) Rectangular coordinates: (-6,0) 
E) Rectangular coordinates: (0,-6)

Question 6

Convert the rectangular equation to polar form.Assume r > 1.​ $y = - 3$ ​

Accepted Answer

A)  $r = - 3 \sec \theta$ 
B)  $r = - 3 \csc \theta$ 
C)  $r = - \csc \theta$ 
D)  $r = - 3 \cos \theta$ 
E)  $r = - 3 \sin \theta$ 
A)  $r = - 3 \sec \theta$ 
B)  $r = - 3 \csc \theta$ 
C)  $r = - \csc \theta$ 
D)  $r = - 3 \cos \theta$ 
E)  $r = - 3 \sin \theta$

Question 7

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places.​ $$( 5,1.5 )$$ ​

Accepted Answer

A) Rectangular coordinates: (4.89,0.35) 
B) Rectangular coordinates: (-4.89,0.35) 
C) Rectangular coordinates: (-0.35,4.89) 
D) Rectangular coordinates: (0.35,4.89) 
E) Rectangular coordinates: (5,1.5) 
A) Rectangular coordinates: (4.89,0.35) 
B) Rectangular coordinates: (-4.89,0.35) 
C) Rectangular coordinates: (-0.35,4.89) 
D) Rectangular coordinates: (0.35,4.89) 
E) Rectangular coordinates: (5,1.5)

Question 8

Convert the polar equation to rectangular form.​ $r ^ { 2 } = 7 \sin \theta$ ​

Accepted Answer

A)  $x ^ { 2 } - y ^ { 2 } - \sqrt [ 3 ] { 49 } y ^ { 2 / 3 } = 0$ 
B)  $x ^ { 2 } + y ^ { 2 } + \sqrt [ 3 ] { 49 } y ^ { 2 / 3 } = 0$ 
C)  $x ^ { 2 } + y ^ { 2 } - \sqrt [ 3 ] { 7 } y ^ { 2 / 3 } = 0$ 
D)  $$x ^ { 2 } + y ^ { 2 } - \sqrt [ 3 ] { 49 } y ^ { 2 / 3 } = 0$$ 
E)  $x ^ { 2 } + y ^ { 2 } + \sqrt [ 3 ] { 7 } y ^ { 2 / 3 } = 0$ 
A)  $x ^ { 2 } - y ^ { 2 } - \sqrt [ 3 ] { 49 } y ^ { 2 / 3 } = 0$ 
B)  $x ^ { 2 } + y ^ { 2 } + \sqrt [ 3 ] { 49 } y ^ { 2 / 3 } = 0$ 
C)  $x ^ { 2 } + y ^ { 2 } - \sqrt [ 3 ] { 7 } y ^ { 2 / 3 } = 0$ 
D)  $$x ^ { 2 } + y ^ { 2 } - \sqrt [ 3 ] { 49 } y ^ { 2 / 3 } = 0$$ 
E)  $x ^ { 2 } + y ^ { 2 } + \sqrt [ 3 ] { 7 } y ^ { 2 / 3 } = 0$

Question 9

Describe the graph of the polar equation and find the corresponding rectangular equation.Select the correct graph.​ $$r = 7 \csc \theta$$ ​

Accepted Answer

A) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​ $$y + 7 = 0$$ ​   
B) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​ $$y - 6 = 0$$ ​   
C) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​ $$y - 9 = 0$$ ​   
D) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​ $$y - 7 = 0$$ ​   
E) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​ $$y - 8 = 0$$ ​   
A) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​ $$y + 7 = 0$$ ​   
B) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​ $$y - 6 = 0$$ ​   
C) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​ $$y - 9 = 0$$ ​   
D) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​ $$y - 7 = 0$$ ​   
E) The graph of the polar equation is not evident by simple inspection.Convert to rectangular form first.​ $$y - 8 = 0$$ ​

Question 10

Convert the rectangular equation to polar form.Assume r > 1.​ $x y = 13$ ​

Accepted Answer

A)  $r ^ { 2 } = 13 \sec 2 \theta$ 
B)  $r ^ { 2 } = 26 \csc 2 \theta$ 
C)  $r ^ { 2 } = 26 \cos 2 \theta$ 
D)  $r ^ { 2 } = 13 \csc 2 \theta$ 
E)  $r ^ { 2 } = 26 \sec 2 \Theta$ 
A)  $r ^ { 2 } = 13 \sec 2 \theta$ 
B)  $r ^ { 2 } = 26 \csc 2 \theta$ 
C)  $r ^ { 2 } = 26 \cos 2 \theta$ 
D)  $r ^ { 2 } = 13 \csc 2 \theta$ 
E)  $r ^ { 2 } = 26 \sec 2 \Theta$

Question 11

A point in rectangular coordinates is given.Convert the point to polar coordinates,r > 0.​ $( - \sqrt { 3 } , - \sqrt { 3 } )$ ​

Accepted Answer

A) Polar coordinates: $\left( \sqrt { 6 } , - \frac { \pi } { 4 } \right)$ 
B) Polar coordinates: $\left( \sqrt { 6 } , - \frac { 5 \pi } { 4 } \right)$ 
C) Polar coordinates: $\left( \sqrt { 6 } , \frac { 5 \pi } { 4 } \right)$ 
D) Polar coordinates: $\left( \sqrt { 6 } , \frac { \pi } { 4 } \right)$ 
E) Polar coordinates: $\left( \sqrt { 6 } , \frac { 3 \pi } { 4 } \right)$ 
A) Polar coordinates: $\left( \sqrt { 6 } , - \frac { \pi } { 4 } \right)$ 
B) Polar coordinates: $\left( \sqrt { 6 } , - \frac { 5 \pi } { 4 } \right)$ 
C) Polar coordinates: $\left( \sqrt { 6 } , \frac { 5 \pi } { 4 } \right)$ 
D) Polar coordinates: $\left( \sqrt { 6 } , \frac { \pi } { 4 } \right)$ 
E) Polar coordinates: $\left( \sqrt { 6 } , \frac { 3 \pi } { 4 } \right)$

Question 12

A point in rectangular coordinates is given.Convert the point to polar coordinates,r > 0.​ $( - 2,0 )$ ​

Accepted Answer

A) ​​Polar coordinates: $( - 2,2 \pi )$ ​ 
B) Polar coordinates: $( - 2 , \pi )$ 
C) Polar coordinates: $$( 2,2 \pi )$$ 
D) Polar coordinates: $$\left( 2 , \frac { \pi } { 2 } \right)$$ 
E) Polar coordinates: $( 2 , \pi )$ 
A) ​​Polar coordinates: $( - 2,2 \pi )$ ​ 
B) Polar coordinates: $( - 2 , \pi )$ 
C) Polar coordinates: $$( 2,2 \pi )$$ 
D) Polar coordinates: $$\left( 2 , \frac { \pi } { 2 } \right)$$ 
E) Polar coordinates: $( 2 , \pi )$

Question 13

A point (a,b)= (r,θ)shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates.​   ​ $$a = 5 , b = - \pi$$ ​

Accepted Answer

A) Rectangular coordinates: (5,0) 
B) Rectangular coordinates: (5,5) 
C) Rectangular coordinates: (-5,5) 
D) Rectangular coordinates: (-5,0) 
E) Rectangular coordinates: (0,5) 
A) Rectangular coordinates: (5,0) 
B) Rectangular coordinates: (5,5) 
C) Rectangular coordinates: (-5,5) 
D) Rectangular coordinates: (-5,0) 
E) Rectangular coordinates: (0,5)

Question 14

Convert the polar equation to rectangular form.​ $r = 10$ ​

Accepted Answer

A)  $x ^ { 2 } + y ^ { 2 } = 100 \mathrm { x }$ 
B)  $$x ^ { 2 } + y ^ { 2 } = 100$$ 
C)  $x ^ { 2 } + y ^ { 2 } = - 100$ 
D)  $x ^ { 2 } + y ^ { 2 } = 100 y$ 
E)  $x ^ { 2 } - y ^ { 2 } = 100$ 
A)  $x ^ { 2 } + y ^ { 2 } = 100 \mathrm { x }$ 
B)  $$x ^ { 2 } + y ^ { 2 } = 100$$ 
C)  $x ^ { 2 } + y ^ { 2 } = - 100$ 
D)  $x ^ { 2 } + y ^ { 2 } = 100 y$ 
E)  $x ^ { 2 } - y ^ { 2 } = 100$

Question 15

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places.​ $$( - 5.7 , - 0.8 )$$ ​

Accepted Answer

A) Rectangular coordinates: (-3.97,5.09) 
B) Rectangular coordinates: (-2.97,5.09) 
C) Rectangular coordinates: (-3.97,4.09) 
D) Rectangular coordinates: (-2.97,4.09) 
E) Rectangular coordinates: (4.09,-3.97) 
A) Rectangular coordinates: (-3.97,5.09) 
B) Rectangular coordinates: (-2.97,5.09) 
C) Rectangular coordinates: (-3.97,4.09) 
D) Rectangular coordinates: (-2.97,4.09) 
E) Rectangular coordinates: (4.09,-3.97)

Question 16

A point in rectangular coordinates is given.Convert the point to polar coordinates,r > 0.​ $( 2,2 )$ ​

Accepted Answer

A) Polar coordinates: $$\left( - \sqrt { 2 } , \frac { \pi } { 4 } \right)$$ 
B) Polar coordinates: $$\left( \sqrt { 8 } , \frac { \pi } { 4 } \right)$$ 
C) Polar coordinates: $$\left( - \sqrt { 8 } , \frac { \pi } { 4 } \right)$$ 
D) Polar coordinates: $\left( \sqrt { 8 } , - \frac { \pi } { 4 } \right)$ 
E) Polar coordinates: $\left( \sqrt { 2 } , \frac { \pi } { 4 } \right)$ 
A) Polar coordinates: $$\left( - \sqrt { 2 } , \frac { \pi } { 4 } \right)$$ 
B) Polar coordinates: $$\left( \sqrt { 8 } , \frac { \pi } { 4 } \right)$$ 
C) Polar coordinates: $$\left( - \sqrt { 8 } , \frac { \pi } { 4 } \right)$$ 
D) Polar coordinates: $\left( \sqrt { 8 } , - \frac { \pi } { 4 } \right)$ 
E) Polar coordinates: $\left( \sqrt { 2 } , \frac { \pi } { 4 } \right)$

Question 17

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

Accepted Answer

A)  $x ^ { 2 } + y ^ { 2 } - 9 x = 0$ 
B)  $x ^ { 2 } + y ^ { 2 } - 9 y = 0$ 
C)  $x ^ { 2 } + y ^ { 2 } + 9 \mathrm { x } = 0$ 
D)  $x ^ { 2 } + y ^ { 2 } + 9 y = 0$ 
E)  $x ^ { 2 } + y ^ { 2 } - 9 = 0$ 
A)  $x ^ { 2 } + y ^ { 2 } - 9 x = 0$ 
B)  $x ^ { 2 } + y ^ { 2 } - 9 y = 0$ 
C)  $x ^ { 2 } + y ^ { 2 } + 9 \mathrm { x } = 0$ 
D)  $x ^ { 2 } + y ^ { 2 } + 9 y = 0$ 
E)  $x ^ { 2 } + y ^ { 2 } - 9 = 0$

Question 18

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places.​ $$( 7.2 , - 3.0 )$$ ​

Accepted Answer

A) Rectangular coordinates: (-7.13,-1.02) 
B) Rectangular coordinates: (-1.02,-7.13) 
C) Rectangular coordinates: (-6.13,-1.02) 
D) Rectangular coordinates: (-7.13,-0.02) 
E) Rectangular coordinates: (-6.13,-0.02) 
A) Rectangular coordinates: (-7.13,-1.02) 
B) Rectangular coordinates: (-1.02,-7.13) 
C) Rectangular coordinates: (-6.13,-1.02) 
D) Rectangular coordinates: (-7.13,-0.02) 
E) Rectangular coordinates: (-6.13,-0.02)

Question 19

Convert the polar equation to rectangular form.​ $r = 3 \cos \theta$ ​

Accepted Answer

A)  $x ^ { 2 } + y ^ { 2 } + 3 y = 0$ 
B)  $x ^ { 2 } + y ^ { 2 } - 3 = 0$ 
C)  $x ^ { 2 } + y ^ { 2 } - 3 y = 0$ 
D)  $x ^ { 2 } + y ^ { 2 } + 3 x = 0$ 
E)  $x ^ { 2 } + y ^ { 2 } - 3 x = 0$ 
A)  $x ^ { 2 } + y ^ { 2 } + 3 y = 0$ 
B)  $x ^ { 2 } + y ^ { 2 } - 3 = 0$ 
C)  $x ^ { 2 } + y ^ { 2 } - 3 y = 0$ 
D)  $x ^ { 2 } + y ^ { 2 } + 3 x = 0$ 
E)  $x ^ { 2 } + y ^ { 2 } - 3 x = 0$

Question 20

Convert the rectangular equation to polar form.Assume r > 1.​ $x = 15$ ​

Accepted Answer

A)  $r = 15 \sec \theta$ 
B)  $r = \csc \theta$ 
C)  $r = 15 \sin \theta$ 
D)  $r = 15 \csc \theta$ 
E)  $r = 15 \cos \theta$ 
A)  $r = 15 \sec \theta$ 
B)  $r = \csc \theta$ 
C)  $r = 15 \sin \theta$ 
D)  $r = 15 \csc \theta$ 
E)  $r = 15 \cos \theta$

Exam 65: Polar Coordinates

Convert the rectangular equation to polar form.Assume r > 1.​ 7x−y+6=07 x - y + 6 = 07x−y+6=0 ​

Use a graphing utility to find one set of polar coordinates for the point given in rectangular coordinates,r > 0.Round your answers to three decimal places.​ (3,−2)( 3 , - 2 )(3,−2) ​

A point in rectangular coordinates is given.Convert the point to polar coordinates,r > 0.​ (0,4)( 0,4 )(0,4) ​

Convert the rectangular equation to polar form.Assume a > 0,r > 1.​ x2+y2−3ay=0x ^ { 2 } + y ^ { 2 } - 3 a y = 0x2+y2−3ay=0 ​

A point (a,b)shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates.​ ​ a=6,b=π2a = 6 , b = \frac { \pi } { 2 }a=6,b=2π​ ​

Convert the rectangular equation to polar form.Assume r > 1.​ y=−3y = - 3y=−3 ​

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places.​ (5,1.5)( 5,1.5 )(5,1.5) ​

Convert the polar equation to rectangular form.​ r2=7sin⁡θr ^ { 2 } = 7 \sin \thetar2=7sinθ ​

Describe the graph of the polar equation and find the corresponding rectangular equation.Select the correct graph.​ r=7csc⁡θr = 7 \csc \thetar=7cscθ ​

Convert the rectangular equation to polar form.Assume r > 1.​ xy=13x y = 13xy=13 ​

A point in rectangular coordinates is given.Convert the point to polar coordinates,r > 0.​ (−3,−3)( - \sqrt { 3 } , - \sqrt { 3 } )(−3​,−3​) ​

A point in rectangular coordinates is given.Convert the point to polar coordinates,r > 0.​ (−2,0)( - 2,0 )(−2,0) ​

A point (a,b)= (r,θ)shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates.​ ​ a=5,b=−πa = 5 , b = - \pia=5,b=−π ​

Convert the polar equation to rectangular form.​ r=10r = 10r=10 ​

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places.​ (−5.7,−0.8)( - 5.7 , - 0.8 )(−5.7,−0.8) ​

A point in rectangular coordinates is given.Convert the point to polar coordinates,r > 0.​ (2,2)( 2,2 )(2,2) ​

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

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places.​ (7.2,−3.0)( 7.2 , - 3.0 )(7.2,−3.0) ​

Convert the polar equation to rectangular form.​ r=3cos⁡θr = 3 \cos \thetar=3cosθ ​

Convert the rectangular equation to polar form.Assume r > 1.​ x=15x = 15x=15 ​

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Convert the rectangular equation to polar form.Assume r > 1. $7 x - y + 6 = 0$

Use a graphing utility to find one set of polar coordinates for the point given in rectangular coordinates,r > 0.Round your answers to three decimal places. $( 3 , - 2 )$

A point in rectangular coordinates is given.Convert the point to polar coordinates,r > 0. $( 0,4 )$

Convert the rectangular equation to polar form.Assume a > 0,r > 1. $x ^ { 2 } + y ^ { 2 } - 3 a y = 0$

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 = 6 , b = \frac { \pi } { 2 } $ $a = 6 , b = \frac { \pi } { 2 }$

Convert the rectangular equation to polar form.Assume r > 1. $y = - 3$

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places. $( 5,1.5 )$

Convert the polar equation to rectangular form. $r ^ { 2 } = 7 \sin \theta$

Describe the graph of the polar equation and find the corresponding rectangular equation.Select the correct graph. $r = 7 \csc \theta$

Convert the rectangular equation to polar form.Assume r > 1. $x y = 13$

A point in rectangular coordinates is given.Convert the point to polar coordinates,r > 0. $( - \sqrt { 3 } , - \sqrt { 3 } )$

A point in rectangular coordinates is given.Convert the point to polar coordinates,r > 0. $( - 2,0 )$

A point (a,b)= (r,θ)shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates. $A point (a,b)= (r,θ)shown in below graph in polar coordinates is given.Convert the point to rectangular coordinates. a = 5 , b = - \pi $ $a = 5 , b = - \pi$

Convert the polar equation to rectangular form. $r = 10$

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places. $( - 5.7 , - 0.8 )$

A point in rectangular coordinates is given.Convert the point to polar coordinates,r > 0. $( 2,2 )$

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

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places. $( 7.2 , - 3.0 )$

Convert the polar equation to rectangular form. $r = 3 \cos \theta$

Convert the rectangular equation to polar form.Assume r > 1. $x = 15$