Question 1

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.
-$$r = \frac { 3 } { 1 - 4 \sin \theta }$$

Accepted Answer

A)  No symmetry 
B)  $x$-axis only 
C)  x-axis, $y$-axis, origin 
D)  $y$-axis only 
A)  No symmetry 
B)  $x$-axis only 
C)  x-axis, $y$-axis, origin 
D)  $y$-axis only

Question 2

Prove that $ \overrightarrow{R S} $ and $ \overrightarrow{O P} $ are equivalent by showing that they represent the same vector.
-R = (-4, -2), S = (-11, -11), O = (7, -3), and P = (-8, -12)

Accepted Answer

A) True 
 B)False

Question 3

Explain how to find parametric equations for a given polar curve. Make up an example of a polar equation and
find the corresponding parametric equations.

Accepted Answer

The parametric equat

Question 4

Write the complex number in the form a + bi.
-$8 \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right)$

Accepted Answer

A)  $4 \sqrt { 3 } + 4 \mathrm { i }$ 
B)  $\frac { 1 } { 4 } + \frac { \sqrt { 3 } } { 4 } \mathrm { i }$ 
C)  $4 + 4 \sqrt { 3 } \mathrm { i }$ 
D)  $\frac { \sqrt { 3 } } { 4 } + \frac { 1 } { 4 } \mathrm { i }$ 
A)  $4 \sqrt { 3 } + 4 \mathrm { i }$ 
B)  $\frac { 1 } { 4 } + \frac { \sqrt { 3 } } { 4 } \mathrm { i }$ 
C)  $4 + 4 \sqrt { 3 } \mathrm { i }$ 
D)  $\frac { \sqrt { 3 } } { 4 } + \frac { 1 } { 4 } \mathrm { i }$

Question 5

Find the component form of the indicated vector.
-Let $\mathbf { u } = \langle - 2,3 \rangle$. Find $- 8 \mathbf { u }$.

Accepted Answer

A)  $\langle - 16,24 \rangle$ 
B)  $\langle - 16 , - 24 \rangle$ 
C)  $\langle 16 , - 24 \rangle$ 
D)  $\langle 16,24 \rangle$ 
A)  $\langle - 16,24 \rangle$ 
B)  $\langle - 16 , - 24 \rangle$ 
C)  $\langle 16 , - 24 \rangle$ 
D)  $\langle 16,24 \rangle$

Question 6

Use De Moivre's Theorem to find the indicated power of the complex number. Write your answer in standard form a + bi.
-$\left( 4 \left( \cos 90 ^ { \circ } + i \sin 90 ^ { \circ } \right) \right) ^ { 5 }$

Accepted Answer

A)  1024 
B)  $1024 \mathrm { i }$ 
C)  $20 \mathrm { i }$ 
D)  0 
A)  1024 
B)  $1024 \mathrm { i }$ 
C)  $20 \mathrm { i }$ 
D)  0

Question 7

Determine two pairs of polar coordinates for the point with 0° ≤θ < 360°.
-$\left( - \frac { 5 \sqrt { 3 } } { 2 } , \frac { 5 } { 2 } \right)$

Accepted Answer

A)  $\left( 5,300 ^ { \circ } \right) , \left( - 5,120 ^ { \circ } \right)$ 
B)  $\left( 5,240 ^ { \circ } \right) , \left( - 5,60 ^ { \circ } \right)$ 
C)  $\left( 5,30 ^ { \circ } \right) , \left( - 5,210 ^ { \circ } \right)$ 
D)  $\left( 5,150 ^ { \circ } \right) , \left( - 5,330 ^ { \circ } \right)$ 
A)  $\left( 5,300 ^ { \circ } \right) , \left( - 5,120 ^ { \circ } \right)$ 
B)  $\left( 5,240 ^ { \circ } \right) , \left( - 5,60 ^ { \circ } \right)$ 
C)  $\left( 5,30 ^ { \circ } \right) , \left( - 5,210 ^ { \circ } \right)$ 
D)  $\left( 5,150 ^ { \circ } \right) , \left( - 5,330 ^ { \circ } \right)$

Question 8

Find the product or quotient. Write the answer in standard form.
-$$\frac { 4 - 3 i } { 5 + 3 i }$$

Accepted Answer

A)  $\frac { 29 } { 16 } + \frac { 27 } { 16 } \mathrm { i }$ 
B)  $\frac { 29 } { 34 } + \frac { 3 } { 34 } \mathrm { i }$ 
C)  $\frac { 11 } { 34 } - \frac { 27 } { 34 } \mathrm { i }$ 
D)  $\frac { 11 } { 16 } + \frac { 27 } { 16 } i$ 
A)  $\frac { 29 } { 16 } + \frac { 27 } { 16 } \mathrm { i }$ 
B)  $\frac { 29 } { 34 } + \frac { 3 } { 34 } \mathrm { i }$ 
C)  $\frac { 11 } { 34 } - \frac { 27 } { 34 } \mathrm { i }$ 
D)  $\frac { 11 } { 16 } + \frac { 27 } { 16 } i$

Question 9

Solve the problem using a graphing calculator.
-Determine the approximate distance that a baseball travels if it is thrown with a velocity of 120 feet per second at an angle of $35 ^ { \circ }$ relative to level ground.

Accepted Answer

A)  296 feet 
B)  4 feet 
C)  423 feet 
D)  $604 \mathrm { feet }$ 
A)  296 feet 
B)  4 feet 
C)  423 feet 
D)  $604 \mathrm { feet }$

Question 10

Find the rectangular coordinates of the point with the given polar coordinates.
-$\left( - 4,240 ^ { \circ } \right)$

Accepted Answer

A)  $( 2 \sqrt { 3 } , 2 )$ 
B)  $( - 2 , - 2 \sqrt { 3 } )$ 
C)  $( - 2 \sqrt { 3 } , - 2 )$ 
D)  $( 2,2 \sqrt { 3 } )$ 
A)  $( 2 \sqrt { 3 } , 2 )$ 
B)  $( - 2 , - 2 \sqrt { 3 } )$ 
C)  $( - 2 \sqrt { 3 } , - 2 )$ 
D)  $( 2,2 \sqrt { 3 } )$

Question 11

Find the indicated roots. Write the answer in polar form.
-Cube roots of $27 \left( \cos 321 ^ { \circ } + i \sin 321 ^ { \circ } \right)$

Accepted Answer

A)  $3 \left( \cos 107 ^ { \circ } + i \sin 107 ^ { \circ } \right) , 3 \left( \cos 227 ^ { \circ } + i \sin 227 ^ { \circ } \right) , 3 \left( \cos 347 ^ { \circ } + i \sin 347 ^ { \circ } \right)$ 
B)  $3 \left( \cos 197 ^ { \circ } + i \sin 197 ^ { \circ } \right) , 3 \left( \cos 257 ^ { \circ } + i \sin 257 ^ { \circ } \right) , 3 \left( \cos 137 ^ { \circ } + i \sin 137 ^ { \circ } \right)$ 
C)  $3 \left( \cos 107 ^ { \circ } + i \sin 107 ^ { \circ } \right) , 3 \left( \cos 167 ^ { \circ } + i \sin 167 ^ { \circ } \right) , 3 \left( \cos 47 ^ { \circ } + i \sin 47 ^ { \circ } \right)$ 
D)  $3 \left( \cos 107 ^ { \circ } + i \sin 107 ^ { \circ } \right) , 3 \left( \cos 227 ^ { \circ } + i \sin 227 ^ { \circ } \right) , 3 \left( \cos 227 ^ { \circ } + i \sin 227 ^ { \circ } \right)$ 
A)  $3 \left( \cos 107 ^ { \circ } + i \sin 107 ^ { \circ } \right) , 3 \left( \cos 227 ^ { \circ } + i \sin 227 ^ { \circ } \right) , 3 \left( \cos 347 ^ { \circ } + i \sin 347 ^ { \circ } \right)$ 
B)  $3 \left( \cos 197 ^ { \circ } + i \sin 197 ^ { \circ } \right) , 3 \left( \cos 257 ^ { \circ } + i \sin 257 ^ { \circ } \right) , 3 \left( \cos 137 ^ { \circ } + i \sin 137 ^ { \circ } \right)$ 
C)  $3 \left( \cos 107 ^ { \circ } + i \sin 107 ^ { \circ } \right) , 3 \left( \cos 167 ^ { \circ } + i \sin 167 ^ { \circ } \right) , 3 \left( \cos 47 ^ { \circ } + i \sin 47 ^ { \circ } \right)$ 
D)  $3 \left( \cos 107 ^ { \circ } + i \sin 107 ^ { \circ } \right) , 3 \left( \cos 227 ^ { \circ } + i \sin 227 ^ { \circ } \right) , 3 \left( \cos 227 ^ { \circ } + i \sin 227 ^ { \circ } \right)$

Question 12

Find the unit vector in the direction of the given vector. Write your answer in the indicated form.
-Let $\mathbf { u } = - 5 \mathbf { i } + 3 \mathbf { j }$. Find the unit vector in the direction of $\mathbf { u }$, and write your answer in component form.

Accepted Answer

A)  $\left( - \frac { 5 } { 8 } , \frac { 3 } { 8 } \right)$ 
B)  $\left( \frac { - 5 } { \sqrt { 34 } } , \frac { 3 } { \sqrt { 34 } } \right)$ 
C)  $\langle 1,1 \rangle$ 
D)  $\left( - \frac { 5 } { 34 } , \frac { 3 } { 34 } \right)$ 
A)  $\left( - \frac { 5 } { 8 } , \frac { 3 } { 8 } \right)$ 
B)  $\left( \frac { - 5 } { \sqrt { 34 } } , \frac { 3 } { \sqrt { 34 } } \right)$ 
C)  $\langle 1,1 \rangle$ 
D)  $\left( - \frac { 5 } { 34 } , \frac { 3 } { 34 } \right)$

Question 13

Determine two pairs of polar coordinates for the point with 0° ≤θ < 360°.
-$( 4,4 )$

Accepted Answer

A)  $\left( 4 \sqrt { 2 } , 225 ^ { \circ } \right) , \left( - 4 \sqrt { 2 } , 45 ^ { \circ } \right)$ 
B)  $\left( 4 \sqrt { 2 } , 135 ^ { \circ } \right) , \left( - 4 \sqrt { 2 } , 315 ^ { \circ } \right)$ 
C)  $\left( 4 \sqrt { 2 } , 315 ^ { \circ } \right) , \left( - 4 \sqrt { 2 } , 135 ^ { \circ } \right)$ 
D)  $\left( 4 \sqrt { 2 } , 45 ^ { \circ } \right) , \left( - 4 \sqrt { 2 } , 225 ^ { \circ } \right)$ 
A)  $\left( 4 \sqrt { 2 } , 225 ^ { \circ } \right) , \left( - 4 \sqrt { 2 } , 45 ^ { \circ } \right)$ 
B)  $\left( 4 \sqrt { 2 } , 135 ^ { \circ } \right) , \left( - 4 \sqrt { 2 } , 315 ^ { \circ } \right)$ 
C)  $\left( 4 \sqrt { 2 } , 315 ^ { \circ } \right) , \left( - 4 \sqrt { 2 } , 135 ^ { \circ } \right)$ 
D)  $\left( 4 \sqrt { 2 } , 45 ^ { \circ } \right) , \left( - 4 \sqrt { 2 } , 225 ^ { \circ } \right)$

Question 14

Prove that $ \overrightarrow{R S} $ and $ \overrightarrow{O P} $ are equivalent by showing that they represent the same vector.
-R = (-1, 3), S = (-10, 5), O = (3, -1), and P = (-6, 1)

Accepted Answer

A) True 
 B)False

Question 15

Choose the graph of the given parametric equations.
-$x=t^{3}+1, y=t^{3}-1,-2 \leq t \leq 2$

Accepted Answer

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

Question 16

Write the vector u as a sum of two orthogonal vectors, one of which is the vector projection of u onto v, $ \operatorname{proj}_{\mathbf{v}} \mathbf{u} $.
-$\mathbf { u } = \langle 8,6 \rangle , \mathbf { v } = \langle 2,4 \rangle$

Accepted Answer

A)  $\langle 4,8 \rangle + \langle 4 , - 2 \rangle$ 
B)  $\langle - 1 , - 2 \rangle + \langle 9 , - 4.5 \rangle$ 
C)  $\langle 2,4 \rangle + \langle 6,2 \rangle$ 
D)  $\langle 3,6 \rangle + \langle 5 , - 2.5 \rangle$ 
A)  $\langle 4,8 \rangle + \langle 4 , - 2 \rangle$ 
B)  $\langle - 1 , - 2 \rangle + \langle 9 , - 4.5 \rangle$ 
C)  $\langle 2,4 \rangle + \langle 6,2 \rangle$ 
D)  $\langle 3,6 \rangle + \langle 5 , - 2.5 \rangle$

Question 17

Find the angle between the given vectors to the nearest tenth of a degree.
-$\mathbf { u } = \sqrt { 5 } \mathbf { i } - 8 \mathbf { j } , \mathbf { v } = \sqrt { 5 } \mathbf { i } + \mathbf { j }$

Accepted Answer

A)  $65.9 ^ { \circ }$ 
B)  $98.5 ^ { \circ }$ 
C)  $33.3 ^ { \circ }$ 
D)  $90.4 ^ { \circ }$ 
A)  $65.9 ^ { \circ }$ 
B)  $98.5 ^ { \circ }$ 
C)  $33.3 ^ { \circ }$ 
D)  $90.4 ^ { \circ }$

Question 18

Find the angle between the given vectors to the nearest tenth of a degree.
-$$\mathbf { u } = \langle - 4,2 \rangle , \mathbf { v } = \langle - 9 , - 3 \rangle$$

Accepted Answer

A)  $12.5 ^ { \circ }$ 
B)  $22.5 ^ { \circ }$ 
C)  $45.0 ^ { \circ }$ 
D)  $55.0 ^ { \circ }$ 
A)  $12.5 ^ { \circ }$ 
B)  $22.5 ^ { \circ }$ 
C)  $45.0 ^ { \circ }$ 
D)  $55.0 ^ { \circ }$

Question 19

Choose the graph of the given parametric equations.
-$x = 7 \sin t + \sin 7 t , y = 7 \cos t + \cos 7 t$

Accepted Answer

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

Question 20

Use De Moivre's Theorem to find the indicated power of the complex number. Write your answer in standard form a + bi.
-$( 2 - 2 i ) ^ { 5 }$

Accepted Answer

A)  $- 64 \sqrt { 2 } + 64 \sqrt { 2 } i$ 
B)  $- 64 + 64 i$ 
C)  $- 128 + 128 \mathrm { i }$ 
D)  $- \sqrt { 2 } + \sqrt { 2 } \mathrm { i }$ 
A)  $- 64 \sqrt { 2 } + 64 \sqrt { 2 } i$ 
B)  $- 64 + 64 i$ 
C)  $- 128 + 128 \mathrm { i }$ 
D)  $- \sqrt { 2 } + \sqrt { 2 } \mathrm { i }$

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. - $r = \frac { 3 } { 1 - 4 \sin \theta }$

Prove that $\overrightarrow{R S}$ and $\overrightarrow{O P}$ are equivalent by showing that they represent the same vector. -R = (-4, -2), S = (-11, -11), O = (7, -3), and P = (-8, -12)

Explain how to find parametric equations for a given polar curve. Make up an example of a polar equation and find the corresponding parametric equations.

Write the complex number in the form a + bi. - $8 \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right)$

Find the component form of the indicated vector. -Let $\mathbf { u } = \langle - 2,3 \rangle$ . Find $- 8 \mathbf { u }$ .

Use De Moivre's Theorem to find the indicated power of the complex number. Write your answer in standard form a + bi. - $\left( 4 \left( \cos 90 ^ { \circ } + i \sin 90 ^ { \circ } \right) \right) ^ { 5 }$

Determine two pairs of polar coordinates for the point with 0° ≤θ < 360°. - $\left( - \frac { 5 \sqrt { 3 } } { 2 } , \frac { 5 } { 2 } \right)$

Find the product or quotient. Write the answer in standard form. - $\frac { 4 - 3 i } { 5 + 3 i }$

Solve the problem using a graphing calculator. -Determine the approximate distance that a baseball travels if it is thrown with a velocity of 120 feet per second at an angle of $35 ^ { \circ }$ relative to level ground.

Find the rectangular coordinates of the point with the given polar coordinates. - $\left( - 4,240 ^ { \circ } \right)$

Find the indicated roots. Write the answer in polar form. -Cube roots of $27 \left( \cos 321 ^ { \circ } + i \sin 321 ^ { \circ } \right)$

Find the unit vector in the direction of the given vector. Write your answer in the indicated form. -Let $\mathbf { u } = - 5 \mathbf { i } + 3 \mathbf { j }$ . Find the unit vector in the direction of $\mathbf { u }$ , and write your answer in component form.

Determine two pairs of polar coordinates for the point with 0° ≤θ < 360°. - $( 4,4 )$

Prove that $\overrightarrow{R S}$ and $\overrightarrow{O P}$ are equivalent by showing that they represent the same vector. -R = (-1, 3), S = (-10, 5), O = (3, -1), and P = (-6, 1)

Choose the graph of the given parametric equations. - $x=t^{3}+1, y=t^{3}-1,-2 \leq t \leq 2$ $Choose the graph of the given parametric equations. - x=t^{3}+1, y=t^{3}-1,-2 \leq t \leq 2$

Write the vector u as a sum of two orthogonal vectors, one of which is the vector projection of u onto v, $\operatorname{proj}_{\mathbf{v}} \mathbf{u}$ . - $\mathbf { u } = \langle 8,6 \rangle , \mathbf { v } = \langle 2,4 \rangle$

Find the angle between the given vectors to the nearest tenth of a degree. - $\mathbf { u } = \sqrt { 5 } \mathbf { i } - 8 \mathbf { j } , \mathbf { v } = \sqrt { 5 } \mathbf { i } + \mathbf { j }$

Find the angle between the given vectors to the nearest tenth of a degree. - $\mathbf { u } = \langle - 4,2 \rangle , \mathbf { v } = \langle - 9 , - 3 \rangle$

Choose the graph of the given parametric equations. - $x = 7 \sin t + \sin 7 t , y = 7 \cos t + \cos 7 t$

Use De Moivre's Theorem to find the indicated power of the complex number. Write your answer in standard form a + bi. - $( 2 - 2 i ) ^ { 5 }$

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Exam 6: Applications of Trigonometry

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. - r=31−4sin⁡θr = \frac { 3 } { 1 - 4 \sin \theta }r=1−4sinθ3​

Prove that RS→ \overrightarrow{R S} RS and OP→ \overrightarrow{O P} OP are equivalent by showing that they represent the same vector. -R = (-4, -2), S = (-11, -11), O = (7, -3), and P = (-8, -12)

Explain how to find parametric equations for a given polar curve. Make up an example of a polar equation and find the corresponding parametric equations.

Write the complex number in the form a + bi. - 8(cos⁡30∘+isin⁡30∘)8 \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right)8(cos30∘+isin30∘)

Find the component form of the indicated vector. -Let u=⟨−2,3⟩\mathbf { u } = \langle - 2,3 \rangleu=⟨−2,3⟩ . Find −8u- 8 \mathbf { u }−8u .

Use De Moivre's Theorem to find the indicated power of the complex number. Write your answer in standard form a + bi. - (4(cos⁡90∘+isin⁡90∘))5\left( 4 \left( \cos 90 ^ { \circ } + i \sin 90 ^ { \circ } \right) \right) ^ { 5 }(4(cos90∘+isin90∘))5

Determine two pairs of polar coordinates for the point with 0° ≤θ < 360°. - (−532,52)\left( - \frac { 5 \sqrt { 3 } } { 2 } , \frac { 5 } { 2 } \right)(−253​​,25​)

Find the product or quotient. Write the answer in standard form. - 4−3i5+3i\frac { 4 - 3 i } { 5 + 3 i }5+3i4−3i​

Solve the problem using a graphing calculator. -Determine the approximate distance that a baseball travels if it is thrown with a velocity of 120 feet per second at an angle of 35∘35 ^ { \circ }35∘ relative to level ground.

Find the rectangular coordinates of the point with the given polar coordinates. - (−4,240∘)\left( - 4,240 ^ { \circ } \right)(−4,240∘)

Find the indicated roots. Write the answer in polar form. -Cube roots of 27(cos⁡321∘+isin⁡321∘)27 \left( \cos 321 ^ { \circ } + i \sin 321 ^ { \circ } \right)27(cos321∘+isin321∘)

Find the unit vector in the direction of the given vector. Write your answer in the indicated form. -Let u=−5i+3j\mathbf { u } = - 5 \mathbf { i } + 3 \mathbf { j }u=−5i+3j . Find the unit vector in the direction of u\mathbf { u }u , and write your answer in component form.

Determine two pairs of polar coordinates for the point with 0° ≤θ < 360°. - (4,4)( 4,4 )(4,4)

Prove that RS→ \overrightarrow{R S} RS and OP→ \overrightarrow{O P} OP are equivalent by showing that they represent the same vector. -R = (-1, 3), S = (-10, 5), O = (3, -1), and P = (-6, 1)

Choose the graph of the given parametric equations. - x=t3+1,y=t3−1,−2≤t≤2x=t^{3}+1, y=t^{3}-1,-2 \leq t \leq 2x=t3+1,y=t3−1,−2≤t≤2

Write the vector u as a sum of two orthogonal vectors, one of which is the vector projection of u onto v, proj⁡vu \operatorname{proj}_{\mathbf{v}} \mathbf{u} projv​u . - u=⟨8,6⟩,v=⟨2,4⟩\mathbf { u } = \langle 8,6 \rangle , \mathbf { v } = \langle 2,4 \rangleu=⟨8,6⟩,v=⟨2,4⟩

Find the angle between the given vectors to the nearest tenth of a degree. - u=5i−8j,v=5i+j\mathbf { u } = \sqrt { 5 } \mathbf { i } - 8 \mathbf { j } , \mathbf { v } = \sqrt { 5 } \mathbf { i } + \mathbf { j }u=5​i−8j,v=5​i+j

Find the angle between the given vectors to the nearest tenth of a degree. - u=⟨−4,2⟩,v=⟨−9,−3⟩\mathbf { u } = \langle - 4,2 \rangle , \mathbf { v } = \langle - 9 , - 3 \rangleu=⟨−4,2⟩,v=⟨−9,−3⟩

Choose the graph of the given parametric equations. - x=7sin⁡t+sin⁡7t,y=7cos⁡t+cos⁡7tx = 7 \sin t + \sin 7 t , y = 7 \cos t + \cos 7 tx=7sint+sin7t,y=7cost+cos7t

Use De Moivre's Theorem to find the indicated power of the complex number. Write your answer in standard form a + bi. - (2−2i)5( 2 - 2 i ) ^ { 5 }(2−2i)5