Question 1

Which of the following is not a polar point representation for the point $( 3 , \pi / 3 )$ ?

Accepted Answer

A)  $( 3,7 \pi / 3 )$ 
B)  $( - 3,4 \pi / 3 )$ 
C)  $( 3,2 \pi / 3 )$ 
D)  $( - 3,10 \pi / 3 )$ 
E)  $( 3,13 n / 3 )$ 
A)  $( 3,7 \pi / 3 )$ 
B)  $( - 3,4 \pi / 3 )$ 
C)  $( 3,2 \pi / 3 )$ 
D)  $( - 3,10 \pi / 3 )$ 
E)  $( 3,13 n / 3 )$

Question 2

Convert the rectangular coordinates to polar coordinates with $r > 0 \text { and } 0 \leq \theta < 2 \pi$ 
 $( - \sqrt { 3 } , - 1 )$

Accepted Answer

The answer of Convert the rectangular coordinates to polar coordinates...

Question 3

Sketch a graph of the rectangular equation. [Hint: First convert the equation to polar coordinates.] $\left( x ^ { 2 } + y ^ { 2 } + 3 y \right) ^ { 2 } = 9 \left( x ^ { 2 } + y ^ { 2 } \right)$

Accepted Answer

The answer of Sketch a graph of the rectangular equation....

Question 4

Write the complex number in polar form. $z = - 1 - i$

Accepted Answer

The answer of Write the complex number in polar form....

Question 5

Convert the point whose polar coordinates are $( \sqrt { 3 } , \pi / 6 )$ to rectangular coordinates

Accepted Answer

A)  $\left( \frac { 3 } { 2 } , \frac { \sqrt { 3 } } { 2 } \right)$ 
B)  $\left( \frac { 3 } { 2 } , \frac { 1 } { 2 } \right)$ 
C)  $( 3 , \sqrt { 3 } )$ 
D)  $( \sqrt { 3 } , \pi / 6 )$ 
E)  $\left( \frac { 2 } { 3 } , \frac { \sqrt { 2 } } { 2 } \right)$ 
A)  $\left( \frac { 3 } { 2 } , \frac { \sqrt { 3 } } { 2 } \right)$ 
B)  $\left( \frac { 3 } { 2 } , \frac { 1 } { 2 } \right)$ 
C)  $( 3 , \sqrt { 3 } )$ 
D)  $( \sqrt { 3 } , \pi / 6 )$ 
E)  $\left( \frac { 2 } { 3 } , \frac { \sqrt { 2 } } { 2 } \right)$

Question 6

Test the polar equation for symmetry with respect to the polar axis, the pole, and the line $\theta = \pi / 2$ . $r = 3 \cos \theta \csc \theta$
I $\text { symmetric about the polar axis }$
II $\text { symmetric about the pole }$
III $\text { symmetric about the line } \theta = \pi / 2$

Accepted Answer

A) I only 
B) I and II 
C)  I and III 
D) II and III 
E)  none of these 
A) I only 
B) I and II 
C)  I and III 
D) II and III 
E)  none of these

Question 7

Write the complex conjugate of z in polar form with argument $\theta$ between 0 and $2 \pi$  $z = - 5 \sqrt { 3 } - 5 i$

Accepted Answer

The answer of Write the complex conjugate of z in...

Question 8

Let $z _ { 1 } = 4 \left( \cos \frac { \pi } { 6 } + i \sin \frac { \pi } { 6 } \right)$ and $z _ { 2 } = 5 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$
) Find $Z _ { 1 } Z _ { 2 }$

Accepted Answer

A)  $20 + i$ 
B)  $20 - 20 i$ 
C)  $20$ 
D)  $0 - 20 i$ 
E) none 
A)  $20 + i$ 
B)  $20 - 20 i$ 
C)  $20$ 
D)  $0 - 20 i$ 
E) none

Question 9

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

Accepted Answer

A)  $\left( x ^ { 2 } + y ^ { 2 } - 3 x \right) ^ { 2 } = 9 \left( x ^ { 2 } + y ^ { 2 } \right)$ 
B)  $x ^ { 2 } + y ^ { 2 } = 9 ( x + y )$ 
C)  $\left( x ^ { 2 } + y ^ { 2 } - x \right) ^ { 2 } = 3 \left( x ^ { 2 } - y ^ { 2 } \right)$ 
D)  $\left( x ^ { 2 } + y ^ { 2 } + 2 x \right) ^ { 2 } = 3 ( x + y )$ 
E) none of these 
A)  $\left( x ^ { 2 } + y ^ { 2 } - 3 x \right) ^ { 2 } = 9 \left( x ^ { 2 } + y ^ { 2 } \right)$ 
B)  $x ^ { 2 } + y ^ { 2 } = 9 ( x + y )$ 
C)  $\left( x ^ { 2 } + y ^ { 2 } - x \right) ^ { 2 } = 3 \left( x ^ { 2 } - y ^ { 2 } \right)$ 
D)  $\left( x ^ { 2 } + y ^ { 2 } + 2 x \right) ^ { 2 } = 3 ( x + y )$ 
E) none of these

Question 10

Convert the point whose polar coordinates are $( 8,5 \pi / 4 )$  to rectangular coordinates.

Accepted Answer

The answer of Convert the point whose polar coordinates are...

Question 11

Convert the rectangular coordinates to polar coordinates with $r > 0 \text { and } 0 \leq \theta < 2 \pi$ $( 0 , - \sqrt { 2 } )$

Accepted Answer

A)  $( 4 , \pi / 2 )$ 
B)  $( \sqrt { 2 } , 3 \pi / 2 )$ 
C)  $( 4,3 \pi / 2 )$ 
D)  $( \sqrt { 2 } , \pi )$ 
E)  $( 4 , \pi )$ 
A)  $( 4 , \pi / 2 )$ 
B)  $( \sqrt { 2 } , 3 \pi / 2 )$ 
C)  $( 4,3 \pi / 2 )$ 
D)  $( \sqrt { 2 } , \pi )$ 
E)  $( 4 , \pi )$

Question 12

Write $z _ { 1 } = 1 - \sqrt { 2 j }$ in polar form then find $1 / z _ { 1 }$

Accepted Answer

The answer of Write \(z _ { 1 } =...

Question 13

Sketch the curve represented by the parametric equations and find its rectangular-coordinate equation. $x = 3 \cos ^ { 2 } t , y = 3 \sin ^ { 2 } t$

Accepted Answer

The answer of Sketch the curve represented by the parametric...

Question 14

Sketch a graph of the polar equation. $r = - 3 \cos 3 \theta$

Accepted Answer

The answer of Sketch a graph of the polar equation....

Question 15

Graph the polar equation $r = 8 \cos \theta$

Accepted Answer

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

Question 16

Graph the polar equation $r = 8 \sin \theta$

Accepted Answer

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

Question 17

Convert the point whose polar coordinates are $( 1 / \sqrt { 2 } , 3 \pi / 4 )$ to rectangular coordinates

Accepted Answer

A)  $\left( \frac { 3 } { 2 } , \frac { \sqrt { 3 } } { 2 } \right)$ 
B)  $\left( - \frac { 1 } { 2 } , \frac { 1 } { 2 } \right)$ 
C)  $( - \sqrt { 2 } , \sqrt { 2 } )$ 
D)  $( \sqrt { 3 } , \sqrt { 2 } )$ 
E)  $( - 1,1 )$ 
A)  $\left( \frac { 3 } { 2 } , \frac { \sqrt { 3 } } { 2 } \right)$ 
B)  $\left( - \frac { 1 } { 2 } , \frac { 1 } { 2 } \right)$ 
C)  $( - \sqrt { 2 } , \sqrt { 2 } )$ 
D)  $( \sqrt { 3 } , \sqrt { 2 } )$ 
E)  $( - 1,1 )$

Question 18

Find the modulus and the argument for the complex number. $z = - i$

Accepted Answer

The answer of Find the modulus and the argument for...

Question 19

Convert the rectangular coordinates to polar coordinates with $r > 0 \text { and } 0 \leq \theta < 2 \pi$ $( - 2 \sqrt { 3 } , - 2 )$

Accepted Answer

A)  $( 4 , \pi / 6 )$ 
B)  $( 4,5 \pi / 3 )$ 
C)  $( 2,11 \pi / 6 )$ 
D)  $( 4,7 \pi / 6 )$ 
E) none of these 
A)  $( 4 , \pi / 6 )$ 
B)  $( 4,5 \pi / 3 )$ 
C)  $( 2,11 \pi / 6 )$ 
D)  $( 4,7 \pi / 6 )$ 
E) none of these

Question 20

Find the rectangular-coordinate equation for the parametric equations given. $x = 2 \cos ^ { 2 } t , y = 2 \sin ^ { 2 } t$

Accepted Answer

A)  $x + y = 2,0 \leq x \leq 2$ 
B)  $x ^ { 2 } + y ^ { 2 } = 4 , \quad 0 \leq x \leq 4$ 
C)  $2 x ^ { 2 } + 2 y ^ { 2 } = 1 , \quad 0 \leq x \leq 2$ 
D)  $x ^ { 2 } + y ^ { 2 } = 2 , \quad 0 \leq x \leq 2$ 
E)  $x ^ { 2 } - y ^ { 2 } = 4$ 
A)  $x + y = 2,0 \leq x \leq 2$ 
B)  $x ^ { 2 } + y ^ { 2 } = 4 , \quad 0 \leq x \leq 4$ 
C)  $2 x ^ { 2 } + 2 y ^ { 2 } = 1 , \quad 0 \leq x \leq 2$ 
D)  $x ^ { 2 } + y ^ { 2 } = 2 , \quad 0 \leq x \leq 2$ 
E)  $x ^ { 2 } - y ^ { 2 } = 4$

Which of the following is not a polar point representation for the point $( 3 , \pi / 3 )$ ?

Convert the rectangular coordinates to polar coordinates with $r > 0 \text { and } 0 \leq \theta < 2 \pi$ $( - \sqrt { 3 } , - 1 )$

Sketch a graph of the rectangular equation. [Hint: First convert the equation to polar coordinates.] $\left( x ^ { 2 } + y ^ { 2 } + 3 y \right) ^ { 2 } = 9 \left( x ^ { 2 } + y ^ { 2 } \right)$

Write the complex number in polar form. $z = - 1 - i$

Convert the point whose polar coordinates are $( \sqrt { 3 } , \pi / 6 )$ to rectangular coordinates

Test the polar equation for symmetry with respect to the polar axis, the pole, and the line $\theta = \pi / 2$ . $r = 3 \cos \theta \csc \theta$ I $\text { symmetric about the polar axis }$ II $\text { symmetric about the pole }$ III $\text { symmetric about the line } \theta = \pi / 2$

Write the complex conjugate of z in polar form with argument $\theta$ between 0 and $2 \pi$ $z = - 5 \sqrt { 3 } - 5 i$

Let $z _ { 1 } = 4 \left( \cos \frac { \pi } { 6 } + i \sin \frac { \pi } { 6 } \right)$ and $z _ { 2 } = 5 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$ ) Find $Z _ { 1 } Z _ { 2 }$

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

Convert the point whose polar coordinates are $( 8,5 \pi / 4 )$ to rectangular coordinates.

Convert the rectangular coordinates to polar coordinates with $r > 0 \text { and } 0 \leq \theta < 2 \pi$ $( 0 , - \sqrt { 2 } )$

Write $z _ { 1 } = 1 - \sqrt { 2 j }$ in polar form then find $1 / z _ { 1 }$

Sketch the curve represented by the parametric equations and find its rectangular-coordinate equation. $x = 3 \cos ^ { 2 } t , y = 3 \sin ^ { 2 } t$

Sketch a graph of the polar equation. $r = - 3 \cos 3 \theta$

Graph the polar equation $r = 8 \cos \theta$

Graph the polar equation $r = 8 \sin \theta$

Convert the point whose polar coordinates are $( 1 / \sqrt { 2 } , 3 \pi / 4 )$ to rectangular coordinates

Find the modulus and the argument for the complex number. $z = - i$

Convert the rectangular coordinates to polar coordinates with $r > 0 \text { and } 0 \leq \theta < 2 \pi$ $( - 2 \sqrt { 3 } , - 2 )$

Find the rectangular-coordinate equation for the parametric equations given. $x = 2 \cos ^ { 2 } t , y = 2 \sin ^ { 2 } t$

Equations and Graphs

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Right Triangle Approach

Trigonometric Functions: Unit Circle Approach

Conic Sections

Polar Coordinates and Parametric Equations

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections

Sequences and Series

Counting and Probability

Filters

Exam 9: Vectors in Two and Three Dimensions

Which of the following is not a polar point representation for the point (3,π/3)( 3 , \pi / 3 )(3,π/3) ?

Convert the rectangular coordinates to polar coordinates with r>0 and 0≤θ<2πr > 0 \text { and } 0 \leq \theta < 2 \pir>0 and 0≤θ<2π (−3,−1)( - \sqrt { 3 } , - 1 )(−3​,−1)

Sketch a graph of the rectangular equation. [Hint: First convert the equation to polar coordinates.] (x2+y2+3y)2=9(x2+y2)\left( x ^ { 2 } + y ^ { 2 } + 3 y \right) ^ { 2 } = 9 \left( x ^ { 2 } + y ^ { 2 } \right)(x2+y2+3y)2=9(x2+y2)

Write the complex number in polar form. z=−1−iz = - 1 - iz=−1−i

Convert the point whose polar coordinates are (3,π/6)( \sqrt { 3 } , \pi / 6 )(3​,π/6) to rectangular coordinates

Write the complex conjugate of z in polar form with argument θ\thetaθ between 0 and 2π2 \pi2π z=−53−5iz = - 5 \sqrt { 3 } - 5 iz=−53​−5i

Convert the polar equation to rectangular coordinates. r+cos⁡θ=3r+ \cos \theta = 3r+cosθ=3

Convert the point whose polar coordinates are (8,5π/4)( 8,5 \pi / 4 )(8,5π/4) to rectangular coordinates.

Convert the rectangular coordinates to polar coordinates with r>0 and 0≤θ<2πr > 0 \text { and } 0 \leq \theta < 2 \pir>0 and 0≤θ<2π (0,−2)( 0 , - \sqrt { 2 } )(0,−2​)

Write z1=1−2jz _ { 1 } = 1 - \sqrt { 2 j }z1​=1−2j​ in polar form then find 1/z11 / z _ { 1 }1/z1​

Sketch the curve represented by the parametric equations and find its rectangular-coordinate equation. x=3cos⁡2t,y=3sin⁡2tx = 3 \cos ^ { 2 } t , y = 3 \sin ^ { 2 } tx=3cos2t,y=3sin2t

Sketch a graph of the polar equation. r=−3cos⁡3θr = - 3 \cos 3 \thetar=−3cos3θ

Graph the polar equation r=8cos⁡θr = 8 \cos \thetar=8cosθ

Graph the polar equation r=8sin⁡θr = 8 \sin \thetar=8sinθ

Convert the point whose polar coordinates are (1/2,3π/4)( 1 / \sqrt { 2 } , 3 \pi / 4 )(1/2​,3π/4) to rectangular coordinates

Find the modulus and the argument for the complex number. z=−iz = - iz=−i

Convert the rectangular coordinates to polar coordinates with r>0 and 0≤θ<2πr > 0 \text { and } 0 \leq \theta < 2 \pir>0 and 0≤θ<2π (−23,−2)( - 2 \sqrt { 3 } , - 2 )(−23​,−2)

Find the rectangular-coordinate equation for the parametric equations given. x=2cos⁡2t,y=2sin⁡2tx = 2 \cos ^ { 2 } t , y = 2 \sin ^ { 2 } tx=2cos2t,y=2sin2t

Equations and Graphs

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Right Triangle Approach

Trigonometric Functions: Unit Circle Approach

Conic Sections

Polar Coordinates and Parametric Equations

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections

Sequences and Series

Counting and Probability

Filters

Which of the following is not a polar point representation for the point $( 3 , \pi / 3 )$ ?

Convert the rectangular coordinates to polar coordinates with $r > 0 \text { and } 0 \leq \theta < 2 \pi$ $( - \sqrt { 3 } , - 1 )$

Sketch a graph of the rectangular equation. [Hint: First convert the equation to polar coordinates.] $\left( x ^ { 2 } + y ^ { 2 } + 3 y \right) ^ { 2 } = 9 \left( x ^ { 2 } + y ^ { 2 } \right)$

Write the complex number in polar form. $z = - 1 - i$

Convert the point whose polar coordinates are $( \sqrt { 3 } , \pi / 6 )$ to rectangular coordinates

Write the complex conjugate of z in polar form with argument $\theta$ between 0 and $2 \pi$ $z = - 5 \sqrt { 3 } - 5 i$

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

Convert the point whose polar coordinates are $( 8,5 \pi / 4 )$ to rectangular coordinates.

Convert the rectangular coordinates to polar coordinates with $r > 0 \text { and } 0 \leq \theta < 2 \pi$ $( 0 , - \sqrt { 2 } )$

Write $z _ { 1 } = 1 - \sqrt { 2 j }$ in polar form then find $1 / z _ { 1 }$

Sketch the curve represented by the parametric equations and find its rectangular-coordinate equation. $x = 3 \cos ^ { 2 } t , y = 3 \sin ^ { 2 } t$

Sketch a graph of the polar equation. $r = - 3 \cos 3 \theta$

Graph the polar equation $r = 8 \cos \theta$

Graph the polar equation $r = 8 \sin \theta$

Convert the point whose polar coordinates are $( 1 / \sqrt { 2 } , 3 \pi / 4 )$ to rectangular coordinates

Find the modulus and the argument for the complex number. $z = - i$

Convert the rectangular coordinates to polar coordinates with $r > 0 \text { and } 0 \leq \theta < 2 \pi$ $( - 2 \sqrt { 3 } , - 2 )$

Find the rectangular-coordinate equation for the parametric equations given. $x = 2 \cos ^ { 2 } t , y = 2 \sin ^ { 2 } t$