Question 1

Convert the polar equation to rectangular form.​ $r = \frac { 8 } { 1 + \sin \theta }$ ​

Accepted Answer

A)  $x ^ { 2 } + 16 y - 64 = 0$ 
B)  $x ^ { 2 } + 16 x + 64 = 0$ 
C)  $x ^ { 2 } + 16 y - 64 x = 0$ 
D)  $x ^ { 2 } + 16 y + 64 = 0$ 
E)  $x ^ { 2 } + 16 - 64 = 0$ 
A)  $x ^ { 2 } + 16 y - 64 = 0$ 
B)  $x ^ { 2 } + 16 x + 64 = 0$ 
C)  $x ^ { 2 } + 16 y - 64 x = 0$ 
D)  $x ^ { 2 } + 16 y + 64 = 0$ 
E)  $x ^ { 2 } + 16 - 64 = 0$

Question 2

A point in rectangular coordinates is given.Convert the point to polar coordinates,r > 0.​ $( 0 , - 6 )$ ​

Accepted Answer

A) Polar coordinates: $\left( - 6 , \frac { 3 \pi } { 2 } \right)$ 
B) Polar coordinates: $\left( 6 , - \frac { \pi } { 2 } \right)$ 
C) Polar coordinates: $\left( 6 , \frac { \pi } { 2 } \right)$ 
D) Polar coordinates: $\left( - 6 , - \frac { \pi } { 2 } \right)$ 
E) Polar coordinates: $\left( 6 , \frac { 3 \pi } { 2 } \right)$ 
A) Polar coordinates: $\left( - 6 , \frac { 3 \pi } { 2 } \right)$ 
B) Polar coordinates: $\left( 6 , - \frac { \pi } { 2 } \right)$ 
C) Polar coordinates: $\left( 6 , \frac { \pi } { 2 } \right)$ 
D) Polar coordinates: $\left( - 6 , - \frac { \pi } { 2 } \right)$ 
E) Polar coordinates: $\left( 6 , \frac { 3 \pi } { 2 } \right)$

Question 3

Convert the rectangular equation to polar form.Assume a > 0,r > 0.​ $x ^ { 2 } + y ^ { 2 } - 5 a x = 0$ ​

Accepted Answer

A)  $r = 5 a \sin \theta$ 
B)  $r = 5 a \cot \Theta$ 
C)  $r = 5 \operatorname { acsc } \theta$ 
D)  $r = 5 a \cos \theta$ 
E)  $r = 5 \operatorname { asec } \theta$ 
A)  $r = 5 a \sin \theta$ 
B)  $r = 5 a \cot \Theta$ 
C)  $r = 5 \operatorname { acsc } \theta$ 
D)  $r = 5 a \cos \theta$ 
E)  $r = 5 \operatorname { asec } \theta$

Question 4

Convert the rectangular equation to polar form.Assume r > 1.​ $5 x + 7 y - 4 = 0$ ​

Accepted Answer

A)  $y = \frac { - 4 } { 5 \cos \Theta - 7 \sin \theta }$ 
B)  $y = \frac { - 4 } { 5 \cos \Theta + 7 \sin \theta }$ 
C)  $y = \frac { 4 } { 5 \cos \Theta - 7 \sin \theta }$ 
D)  $y = \frac { 4 } { 5 \cos \Theta + 7 \sin \theta }$ 
E)  $y = \frac { 1 } { 5 \cos \Theta + 7 \sin \theta }$ 
A)  $y = \frac { - 4 } { 5 \cos \Theta - 7 \sin \theta }$ 
B)  $y = \frac { - 4 } { 5 \cos \Theta + 7 \sin \theta }$ 
C)  $y = \frac { 4 } { 5 \cos \Theta - 7 \sin \theta }$ 
D)  $y = \frac { 4 } { 5 \cos \Theta + 7 \sin \theta }$ 
E)  $y = \frac { 1 } { 5 \cos \Theta + 7 \sin \theta }$

Question 5

Convert the polar equation to rectangular form.​ $r = - 5 \cos \theta$ ​

Accepted Answer

A)  $x ^ { 2 } + y ^ { 2 } - 5 x = 0$ 
B)  $x ^ { 2 } + y ^ { 2 } - 5 = 0$ 
C)  $x ^ { 2 } + y ^ { 2 } + 5 x = 0$ 
D)  $x ^ { 2 } + y ^ { 2 } - 5 y = 0$ 
E)  $x ^ { 2 } + y ^ { 2 } + 5 y = 0$ 
A)  $x ^ { 2 } + y ^ { 2 } - 5 x = 0$ 
B)  $x ^ { 2 } + y ^ { 2 } - 5 = 0$ 
C)  $x ^ { 2 } + y ^ { 2 } + 5 x = 0$ 
D)  $x ^ { 2 } + y ^ { 2 } - 5 y = 0$ 
E)  $x ^ { 2 } + y ^ { 2 } + 5 y = 0$

Question 6

A point in rectangular coordinates is given.Convert the point to polar coordinates,r > 0.​ $( - 13 , - 13 )$ ​

Accepted Answer

A) Polar coordinates: $\left( \sqrt { 338 } , \frac { 5 \pi } { 4 } \right)$ 
B) Polar coordinates: $\left( - \sqrt { 338 } , \frac { 5 \pi } { 4 } \right)$ 
C) Polar coordinates: $\left( - \sqrt { 13 } , \frac { \pi } { 4 } \right)$ 
D) Polar coordinates: $\left( \sqrt { 13 } , \frac { \pi } { 4 } \right)$ 
E) Polar coordinates: $\left( \sqrt { 338 } , - \frac { \pi } { 4 } \right)$ 
A) Polar coordinates: $\left( \sqrt { 338 } , \frac { 5 \pi } { 4 } \right)$ 
B) Polar coordinates: $\left( - \sqrt { 338 } , \frac { 5 \pi } { 4 } \right)$ 
C) Polar coordinates: $\left( - \sqrt { 13 } , \frac { \pi } { 4 } \right)$ 
D) Polar coordinates: $\left( \sqrt { 13 } , \frac { \pi } { 4 } \right)$ 
E) Polar coordinates: $\left( \sqrt { 338 } , - \frac { \pi } { 4 } \right)$

Question 7

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places.​ $$\left( 2 , \frac { 2 \pi } { 15 } \right)$$ ​

Accepted Answer

A) Rectangular coordinates: (1.83,-0.81) 
B) Rectangular coordinates: (1.83,1.83) 
C) Rectangular coordinates: (-0.81,0.81) 
D) Rectangular coordinates: (1.83,0.15) 
E) Rectangular coordinates: (1.83,0.81) 
A) Rectangular coordinates: (1.83,-0.81) 
B) Rectangular coordinates: (1.83,1.83) 
C) Rectangular coordinates: (-0.81,0.81) 
D) Rectangular coordinates: (1.83,0.15) 
E) Rectangular coordinates: (1.83,0.81)

Question 8

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

Accepted Answer

A) Polar coordinates: $( 0 , - 2 )$ 
B) Polar coordinates: $( 0,2 )$ 
C) Polar coordinates: $( - 2,2 )$ 
D) Polar coordinates: $( - 2,0 )$ 
E) Polar coordinates: $( 2,0 )$ 
A) Polar coordinates: $( 0 , - 2 )$ 
B) Polar coordinates: $( 0,2 )$ 
C) Polar coordinates: $( - 2,2 )$ 
D) Polar coordinates: $( - 2,0 )$ 
E) Polar coordinates: $( 2,0 )$

Question 9

A point in rectangular coordinates is given.Convert the point to polar coordinates.Round your answers to two decimal places,r > 0.​ $( 11,13 )$ ​

Accepted Answer

A) Polar coordinates: $( \sqrt { 290 } , - 0.87 )$ 
B) Polar coordinates: $( \sqrt { 11 } , - 0.87 )$ 
C) Polar coordinates: $( \sqrt { 13 } , 0.87 )$ 
D) Polar coordinates: $( \sqrt { 11 } , 0.87 )$ 
E) Polar coordinates: $( \sqrt { 290 } , 0.87 )$ 
A) Polar coordinates: $( \sqrt { 290 } , - 0.87 )$ 
B) Polar coordinates: $( \sqrt { 11 } , - 0.87 )$ 
C) Polar coordinates: $( \sqrt { 13 } , 0.87 )$ 
D) Polar coordinates: $( \sqrt { 11 } , 0.87 )$ 
E) Polar coordinates: $( \sqrt { 290 } , 0.87 )$

Question 10

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places.​ $$( 5.8,2.62 )$$ ​

Accepted Answer

A) Rectangular coordinates: (-5.03,2.89) 
B) Rectangular coordinates: (5.80,2.89) 
C) Rectangular coordinates: (2.89,-5.03) 
D) Rectangular coordinates: (-4.03,3.89) 
E) Rectangular coordinates: (3.89,-4.03) 
A) Rectangular coordinates: (-5.03,2.89) 
B) Rectangular coordinates: (5.80,2.89) 
C) Rectangular coordinates: (2.89,-5.03) 
D) Rectangular coordinates: (-4.03,3.89) 
E) Rectangular coordinates: (3.89,-4.03)

Exam 65: Polar Coordinates

Convert the polar equation to rectangular form.​ r=81+sin⁡θr = \frac { 8 } { 1 + \sin \theta }r=1+sinθ8​ ​

A point in rectangular coordinates is given.Convert the point to polar coordinates,r > 0.​ (0,−6)( 0 , - 6 )(0,−6) ​

Convert the rectangular equation to polar form.Assume a > 0,r > 0.​ x2+y2−5ax=0x ^ { 2 } + y ^ { 2 } - 5 a x = 0x2+y2−5ax=0 ​

Convert the rectangular equation to polar form.Assume r > 1.​ 5x+7y−4=05 x + 7 y - 4 = 05x+7y−4=0 ​

Convert the polar equation to rectangular form.​ r=−5cos⁡θr = - 5 \cos \thetar=−5cosθ ​

A point in rectangular coordinates is given.Convert the point to polar coordinates,r > 0.​ (−13,−13)( - 13 , - 13 )(−13,−13) ​

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places.​ (2,2π15)\left( 2 , \frac { 2 \pi } { 15 } \right)(2,152π​) ​

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

A point in rectangular coordinates is given.Convert the point to polar coordinates.Round your answers to two decimal places,r > 0.​ (11,13)( 11,13 )(11,13) ​

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places.​ (5.8,2.62)( 5.8,2.62 )(5.8,2.62) ​

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Convert the polar equation to rectangular form. $r = \frac { 8 } { 1 + \sin \theta }$

A point in rectangular coordinates is given.Convert the point to polar coordinates,r > 0. $( 0 , - 6 )$

Convert the rectangular equation to polar form.Assume a > 0,r > 0. $x ^ { 2 } + y ^ { 2 } - 5 a x = 0$

Convert the rectangular equation to polar form.Assume r > 1. $5 x + 7 y - 4 = 0$

Convert the polar equation to rectangular form. $r = - 5 \cos \theta$

A point in rectangular coordinates is given.Convert the point to polar coordinates,r > 0. $( - 13 , - 13 )$

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places. $\left( 2 , \frac { 2 \pi } { 15 } \right)$

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

A point in rectangular coordinates is given.Convert the point to polar coordinates.Round your answers to two decimal places,r > 0. $( 11,13 )$

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places. $( 5.8,2.62 )$