Question 1

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

Accepted Answer

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

Question 2

Find a rectangular-coordinate equation for the curve by eliminating the parameter. $x = t + 3 , y = \frac { t } { t + 3 }$

Accepted Answer

A)  $y = \frac { x - 4 } { x }$ 
B)  $y = \frac { x - 3 } { x }$ 
C)  $y = \frac { x - 2 } { 3 x }$ 
D)  $y = \frac { 2 x - 1 } { 2 x }$ 
E)  none of these 
A)  $y = \frac { x - 4 } { x }$ 
B)  $y = \frac { x - 3 } { x }$ 
C)  $y = \frac { x - 2 } { 3 x }$ 
D)  $y = \frac { 2 x - 1 } { 2 x }$ 
E)  none of these

Question 3

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 4

Convert the equation to polar form. $x ^ { 2 } - y ^ { 2 } = 9$

Accepted Answer

The answer of Convert the equation to polar form. \(x...

Question 5

Test the polar equation for symmetry with respect to the polar axis, the pole, and the line $\theta = \pi / 2$ . $r = 5 \sec \theta$

Accepted Answer

symmetric

Question 6

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 7

Find a rectangular-coordinate equation for the curve by eliminating the parameter. $x = 16 - t ^ { 2 } , y = 4 + t$

Accepted Answer

The answer of Find a rectangular-coordinate equation for the curve...

Question 8

Convert the rectangular coordinates to polar coordinates with $r > 0 \text { and } 0 \leq \theta < 2 \pi$ 
 $( 0 , - \sqrt { 5 } )$

Accepted Answer

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

Question 9

Find parametric equations for the line with the given properties.Passing through $( 12,8 )$ and the origin

Accepted Answer

A)  $x = 3 t , y = - 2 t / 3$ 
B)  $x = 12 t , y = 3 t / 2$ 
C)  $x = t , y = - 3 t / 2 + 8$ 
D)  $x = 3 t / 2 , y = t + 12$ 
E) none of these 
A)  $x = 3 t , y = - 2 t / 3$ 
B)  $x = 12 t , y = 3 t / 2$ 
C)  $x = t , y = - 3 t / 2 + 8$ 
D)  $x = 3 t / 2 , y = t + 12$ 
E) none of these

Question 10

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

Accepted Answer

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

Question 11

Use DeMoivre's Theorem to find the indicated power. $( \sqrt { 3 } - 3 i ) ^ { 3 }$

Accepted Answer

A)  $- 24 + \sqrt { 3 } i$ 
B)  $- 24 \sqrt { 3 }$ 
C)  $- 24 i$ 
D)  $- \sqrt { 3 } i$ 
E)  $24 - \sqrt { 3 } i$ 
A)  $- 24 + \sqrt { 3 } i$ 
B)  $- 24 \sqrt { 3 }$ 
C)  $- 24 i$ 
D)  $- \sqrt { 3 } i$ 
E)  $24 - \sqrt { 3 } i$

Question 12

Use DeMoivre's Theorem to find the indicated power. $( 1 - \sqrt { 3 } i ) ^ { 5 }$

Accepted Answer

The answer of Use DeMoivre's Theorem to find the indicated...

Question 13

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

Accepted Answer

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

Question 14

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

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

Question 15

Find two polar coordinate representations for the point $( 3 , \pi / 3 )$ , one with $r > 0$ , and the other with $r < 0$

Accepted Answer

The answer of Find two polar coordinate representations for the...

Question 16

Test the polar equation for symmetry with respect to the polar axis, the pole, and the line $\theta = \pi / 2$ . $r ^ { 2 } = 9 \cos 2 \theta$
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)  I, II, III 
A) I only 
B) I and II 
C)  I and III 
D) II and III 
E)  I, II, III

Question 17

Convert the polar equation to rectangular coordinates. $\frac { y } { 3 } = \csc \theta$

Accepted Answer

A)  $y = 3 x$ 
B)  $x = 3$ 
C)  $x y = 3$ 
D)  $y = 3 x + 1$ 
E) none of these 
A)  $y = 3 x$ 
B)  $x = 3$ 
C)  $x y = 3$ 
D)  $y = 3 x + 1$ 
E) none of these

Question 18

Find the modulus and the argument for the complex number. $z = - 10 i$

Accepted Answer

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

Question 19

If a projectile is fired with an initial speed of $v _ { 0 }$ ft/s at an angle $\alpha$ 
above the horizontal, then its position after t seconds is given by the parametric equations $x = \left( v _ { 0 } \cos \alpha \right) t \text { and } y = \left( v _ { 0 } \sin \alpha \right) t - 16 t ^ { 2 }$ 
where x and y are measured in feet.Suppose a gun fires a bullet into the air with an initial speed of 1024 ft/s at an angle of $30 ^ { \circ }$ to the horizontal. What is the maximum height attained by the bullet?

Accepted Answer

The answer of If a projectile is fired with an...

Question 20

Write the complex number in polar form. $z = - 1 - \sqrt { 3 } i$

Accepted Answer

A)  $z = 2 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$ 
B)  $z = 2 \left( \cos \frac { 4 \pi } { 3 } + i \sin \frac { 4 \pi } { 3 } \right)$ 
C)  $z = 2 \left( \cos \frac { 5 \pi } { 6 } + i \sin \frac { 5 \pi } { 6 } \right)$ 
D)  $z = 2 \left( \cos \frac { 11 \pi } { 6 } + i \sin \frac { 11 \pi } { 6 } \right)$ 
E)  $z = 2 \left( \cos \frac { 5 \pi } { 3 } + i \sin \frac { 5 \pi } { 3 } \right)$ 
A)  $z = 2 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$ 
B)  $z = 2 \left( \cos \frac { 4 \pi } { 3 } + i \sin \frac { 4 \pi } { 3 } \right)$ 
C)  $z = 2 \left( \cos \frac { 5 \pi } { 6 } + i \sin \frac { 5 \pi } { 6 } \right)$ 
D)  $z = 2 \left( \cos \frac { 11 \pi } { 6 } + i \sin \frac { 11 \pi } { 6 } \right)$ 
E)  $z = 2 \left( \cos \frac { 5 \pi } { 3 } + i \sin \frac { 5 \pi } { 3 } \right)$

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

Find a rectangular-coordinate equation for the curve by eliminating the parameter. $x = t + 3 , y = \frac { t } { t + 3 }$

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

Convert the equation to polar form. $x ^ { 2 } - y ^ { 2 } = 9$

Test the polar equation for symmetry with respect to the polar axis, the pole, and the line $\theta = \pi / 2$ . $r = 5 \sec \theta$

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

Find a rectangular-coordinate equation for the curve by eliminating the parameter. $x = 16 - t ^ { 2 } , y = 4 + t$

Convert the rectangular coordinates to polar coordinates with $r > 0 \text { and } 0 \leq \theta < 2 \pi$ $( 0 , - \sqrt { 5 } )$

Find parametric equations for the line with the given properties.Passing through $( 12,8 )$ and the origin

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

Use DeMoivre's Theorem to find the indicated power. $( \sqrt { 3 } - 3 i ) ^ { 3 }$

Use DeMoivre's Theorem to find the indicated power. $( 1 - \sqrt { 3 } i ) ^ { 5 }$

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

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

Find two polar coordinate representations for the point $( 3 , \pi / 3 )$ , one with $r > 0$ , and the other with $r < 0$

Test the polar equation for symmetry with respect to the polar axis, the pole, and the line $\theta = \pi / 2$ . $r ^ { 2 } = 9 \cos 2 \theta$ I $\text { symmetric about the polar axis }$ II $\text { symmetric about the pole }$ III $\text { symmetric about the line } \theta = \pi / 2$

Convert the polar equation to rectangular coordinates. $\frac { y } { 3 } = \csc \theta$

Find the modulus and the argument for the complex number. $z = - 10 i$

Write the complex number in polar form. $z = - 1 - \sqrt { 3 } i$

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

Sketch a graph of the polar equation. r=3−cos⁡θr = \sqrt { 3 } - \cos \thetar=3​−cosθ

Find a rectangular-coordinate equation for the curve by eliminating the parameter. x=t+3,y=tt+3x = t + 3 , y = \frac { t } { t + 3 }x=t+3,y=t+3t​

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

Convert the equation to polar form. x2−y2=9x ^ { 2 } - y ^ { 2 } = 9x2−y2=9

Test the polar equation for symmetry with respect to the polar axis, the pole, and the line θ=π/2\theta = \pi / 2θ=π/2 . r=5sec⁡θr = 5 \sec \thetar=5secθ

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

Find a rectangular-coordinate equation for the curve by eliminating the parameter. x=16−t2,y=4+tx = 16 - t ^ { 2 } , y = 4 + tx=16−t2,y=4+t

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,−5)( 0 , - \sqrt { 5 } )(0,−5​)

Find parametric equations for the line with the given properties.Passing through (12,8)( 12,8 )(12,8) and the origin

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

Use DeMoivre's Theorem to find the indicated power. (3−3i)3( \sqrt { 3 } - 3 i ) ^ { 3 }(3​−3i)3

Use DeMoivre's Theorem to find the indicated power. (1−3i)5( 1 - \sqrt { 3 } i ) ^ { 5 }(1−3​i)5

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​)

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)

Find two polar coordinate representations for the point (3,π/3)( 3 , \pi / 3 )(3,π/3) , one with r>0r > 0r>0 , and the other with r<0r < 0r<0

Convert the polar equation to rectangular coordinates. y3=csc⁡θ\frac { y } { 3 } = \csc \theta3y​=cscθ

Find the modulus and the argument for the complex number. z=−10iz = - 10 iz=−10i

Write the complex number in polar form. z=−1−3iz = - 1 - \sqrt { 3 } iz=−1−3​i

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

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

Find a rectangular-coordinate equation for the curve by eliminating the parameter. $x = t + 3 , y = \frac { t } { t + 3 }$

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

Convert the equation to polar form. $x ^ { 2 } - y ^ { 2 } = 9$

Test the polar equation for symmetry with respect to the polar axis, the pole, and the line $\theta = \pi / 2$ . $r = 5 \sec \theta$

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

Find a rectangular-coordinate equation for the curve by eliminating the parameter. $x = 16 - t ^ { 2 } , y = 4 + t$

Convert the rectangular coordinates to polar coordinates with $r > 0 \text { and } 0 \leq \theta < 2 \pi$ $( 0 , - \sqrt { 5 } )$

Find parametric equations for the line with the given properties.Passing through $( 12,8 )$ and the origin

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

Use DeMoivre's Theorem to find the indicated power. $( \sqrt { 3 } - 3 i ) ^ { 3 }$

Use DeMoivre's Theorem to find the indicated power. $( 1 - \sqrt { 3 } i ) ^ { 5 }$

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

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

Find two polar coordinate representations for the point $( 3 , \pi / 3 )$ , one with $r > 0$ , and the other with $r < 0$

Convert the polar equation to rectangular coordinates. $\frac { y } { 3 } = \csc \theta$

Find the modulus and the argument for the complex number. $z = - 10 i$

Write the complex number in polar form. $z = - 1 - \sqrt { 3 } i$