Question 1

Write the complex number in rectangular form.
-5.62( $\left. \cos 20 ^ { \circ } + i \sin 20 ^ { \circ } \right)$

Accepted Answer

A)  $- 2.2 - 0.8 \mathrm { i }$ 
B)  $5.3 + 1.9 \mathrm { i }$ 
C)  $1.9 + 5.3 \mathrm { i }$ 
D)  $2.2 + 0.8 \mathrm { i }$ 
A)  $- 2.2 - 0.8 \mathrm { i }$ 
B)  $5.3 + 1.9 \mathrm { i }$ 
C)  $1.9 + 5.3 \mathrm { i }$ 
D)  $2.2 + 0.8 \mathrm { i }$

Question 2

Find sum of the pair of complex numbers.
-$5 + 4 \mathrm { i } , 6$

Accepted Answer

A)  $11 + 4 i$ 
B)  $- 1 + 10 \mathrm { i }$ 
C)  $- 1 + 4 \mathrm { i }$ 
D)  $11 + 10 \mathrm { i }$ 
A)  $11 + 4 i$ 
B)  $- 1 + 10 \mathrm { i }$ 
C)  $- 1 + 4 \mathrm { i }$ 
D)  $11 + 10 \mathrm { i }$

Question 3

Determine two pairs of polar coordinates for the point with 0° ≤ θ < 360°.
-$( 3,3 )$

Accepted Answer

A)  $\left( 3 \sqrt { 2 } , 315 ^ { \circ } \right) , \left( - 3 \sqrt { 2 } , 135 ^ { \circ } \right)$ 
B)  $\left( 3 \sqrt { 2 } , 225 ^ { \circ } \right) , \left( - 3 \sqrt { 2 } , 45 ^ { \circ } \right)$ 
C)  $\left( 3 \sqrt { 2 } , 45 ^ { \circ } \right) , \left( - 3 \sqrt { 2 } , 225 ^ { \circ } \right)$ 
D)  $\left( 3 \sqrt { 2 } , 135 ^ { \circ } \right) , \left( - 3 \sqrt { 2 } , 315 ^ { \circ } \right)$ 
A)  $\left( 3 \sqrt { 2 } , 315 ^ { \circ } \right) , \left( - 3 \sqrt { 2 } , 135 ^ { \circ } \right)$ 
B)  $\left( 3 \sqrt { 2 } , 225 ^ { \circ } \right) , \left( - 3 \sqrt { 2 } , 45 ^ { \circ } \right)$ 
C)  $\left( 3 \sqrt { 2 } , 45 ^ { \circ } \right) , \left( - 3 \sqrt { 2 } , 225 ^ { \circ } \right)$ 
D)  $\left( 3 \sqrt { 2 } , 135 ^ { \circ } \right) , \left( - 3 \sqrt { 2 } , 315 ^ { \circ } \right)$

Question 4

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations.
-$x = \sin t , y = \cos t ; t = \pi$

Accepted Answer

A)  $( 1,0 )$ 
B)  $( 0,1 )$ 
C)  $( 0 , - 1 )$ 
D)  $( - 1,0 )$ 
A)  $( 1,0 )$ 
B)  $( 0,1 )$ 
C)  $( 0 , - 1 )$ 
D)  $( - 1,0 )$

Question 5

Find the angle between the pair of vectors to the nearest tenth of a degree.
-$$\langle - 5 , - 7 \rangle , \langle 6 , - 4 \rangle$$

Accepted Answer

A)  $45.9 ^ { \circ }$ 
B)  $91.8 ^ { \circ }$ 
C)  $101.8 ^ { \circ }$ 
D)  $35.9 ^ { \circ }$ 
A)  $45.9 ^ { \circ }$ 
B)  $91.8 ^ { \circ }$ 
C)  $101.8 ^ { \circ }$ 
D)  $35.9 ^ { \circ }$

Question 6

Solve the problem.
-Two boats are pulling a disabled vessel toward the landing dock with forces of $930 \mathrm { lb }$ and $890 \mathrm { lb }$. The angle between the forces is $28.6 ^ { \circ }$. Find the direction and magnitude of the equilibrant.

Accepted Answer

A)  $1764 \mathrm { lb }$ at an angle of $166.0 ^ { \circ }$ with the 930 -lb force 
B)  $1764 \mathrm { lb }$ at an angle of $76.0 ^ { \circ }$ with the 890 -lb force 
C)  $176 \mathrm { lb }$ at an angle of $166.0 ^ { \circ }$ with the 930 -lb force 
D)  $1764 \mathrm { lb }$ at an angle of $14.0 ^ { \circ }$ with the 930 -lb force 
A)  $1764 \mathrm { lb }$ at an angle of $166.0 ^ { \circ }$ with the 930 -lb force 
B)  $1764 \mathrm { lb }$ at an angle of $76.0 ^ { \circ }$ with the 890 -lb force 
C)  $176 \mathrm { lb }$ at an angle of $166.0 ^ { \circ }$ with the 930 -lb force 
D)  $1764 \mathrm { lb }$ at an angle of $14.0 ^ { \circ }$ with the 930 -lb force

Question 7

Plot the point.
-$$\left( - 4 , \frac { - 5 \pi } { 4 } \right)$$

Accepted Answer

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

Question 8

The graph of a polar equation is given. Select the polar equation for the graph.
-

Accepted Answer

A)  $r = \frac { 3 \cos \theta } { 2 \sin \theta }$ 
B)  $r = \frac { 1 } { 3 \cos \theta - 2 \sin \theta }$ 
C)  $r = \frac { 1 } { 3 \cos \theta + 2 \sin \theta }$ 
D)  $r = \frac { 1 } { 2 \cos \theta + 3 \sin \theta }$ 
A)  $r = \frac { 3 \cos \theta } { 2 \sin \theta }$ 
B)  $r = \frac { 1 } { 3 \cos \theta - 2 \sin \theta }$ 
C)  $r = \frac { 1 } { 3 \cos \theta + 2 \sin \theta }$ 
D)  $r = \frac { 1 } { 2 \cos \theta + 3 \sin \theta }$

Question 9

Find a rectangular equation for the plane curve defined by the parametric equations.
-$$x = t ^ { 2 } + 1 , y = t ^ { 2 } - 1$$

Accepted Answer

A)  $y = x + 2 , x \geq 1$ 
B)  $y = x - 2 , x \geq 1$ 
C)  $y = x ^ { 2 } - 2 , x \geq 1$ 
D)  $y = x ^ { 2 } + 2 , x \geq 1$ 
A)  $y = x + 2 , x \geq 1$ 
B)  $y = x - 2 , x \geq 1$ 
C)  $y = x ^ { 2 } - 2 , x \geq 1$ 
D)  $y = x ^ { 2 } + 2 , x \geq 1$

Question 10

Plot the point.
-$$\left( 4 , \frac { - 3 \pi } { 4 } \right)$$

Accepted Answer

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

Question 11

Graph the polar equation for θ in [0°, 360°).
-$$r = 7 + 7 \sin \theta$$

Accepted Answer

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

Question 12

Find the dot product for the pair of vectors.
-$$\langle 3,0 \rangle , \langle 18 , - 2 \rangle$$

Accepted Answer

A)  54 
B)  $- 6$ 
C)  52 
D)  56 
A)  54 
B)  $- 6$ 
C)  52 
D)  56

Question 13

Solve the problem.
-Two ships leave a harbor together traveling on courses that have an angle of $123 ^ { \circ }$ between them. they each travel 506 miles, how far apart are they (to the nearest mile)?

Accepted Answer

A)  $483 \mathrm { mi }$ 
B)  $40 \mathrm { mi }$ 
C)  $889 \mathrm { mi }$ 
D)  $1778 \mathrm { mi }$ 
A)  $483 \mathrm { mi }$ 
B)  $40 \mathrm { mi }$ 
C)  $889 \mathrm { mi }$ 
D)  $1778 \mathrm { mi }$

Question 14

Find the missing parts of the triangle.
-$$\begin{array} { l } 
\mathrm { A } = 65.3 ^ { \circ } \
\mathrm { a } = 2.15 \mathrm {~km} \
\mathrm {~b} = 2.25 \mathrm {~km}
\end{array}$$
If necessary, round angles to the nearest tenth and side lengths to the nearest hundredth.

Accepted Answer

A)  no such triangle 
B)  $\mathrm { B } = 71.9 ^ { \circ } , \mathrm { C } = 42.8 ^ { \circ } , \mathrm { c } = 1.61 \mathrm {~km}$ 
C)  $\mathrm { B } _ { 1 } = 71.9 ^ { \circ } , \mathrm { C } _ { 1 } = 42.8 ^ { \circ } , \mathrm { c } _ { 1 } = 1.61 \mathrm {~km}$ 
D)  $\mathrm { B } _ { 1 } = 42.8 ^ { \circ } , \mathrm { C } _ { 1 } = 71.9 ^ { \circ } , \mathrm { c } 1 = 1.61 \mathrm {~km}$ $\mathrm { B } _ { 2 } = 108.1 ^ { \circ } , \mathrm { C } _ { 2 } = 6.6 ^ { \circ } , \mathrm { c } _ { 2 } = 0.27 \mathrm {~km}$ $\mathrm { B } _ { 2 } = 6.6 ^ { \circ } , \mathrm { C } _ { 2 } = 108.1 ^ { \circ } , \mathrm { c } _ { 2 } = 0.27 \mathrm {~km}$ 
A)  no such triangle 
B)  $\mathrm { B } = 71.9 ^ { \circ } , \mathrm { C } = 42.8 ^ { \circ } , \mathrm { c } = 1.61 \mathrm {~km}$ 
C)  $\mathrm { B } _ { 1 } = 71.9 ^ { \circ } , \mathrm { C } _ { 1 } = 42.8 ^ { \circ } , \mathrm { c } _ { 1 } = 1.61 \mathrm {~km}$ 
D)  $\mathrm { B } _ { 1 } = 42.8 ^ { \circ } , \mathrm { C } _ { 1 } = 71.9 ^ { \circ } , \mathrm { c } 1 = 1.61 \mathrm {~km}$ $\mathrm { B } _ { 2 } = 108.1 ^ { \circ } , \mathrm { C } _ { 2 } = 6.6 ^ { \circ } , \mathrm { c } _ { 2 } = 0.27 \mathrm {~km}$ $\mathrm { B } _ { 2 } = 6.6 ^ { \circ } , \mathrm { C } _ { 2 } = 108.1 ^ { \circ } , \mathrm { c } _ { 2 } = 0.27 \mathrm {~km}$

Question 15

The graph of r = aθ in polar coordinates is an example of the spiral of Archimedes. With your calculator set to radian
mode, use the given value of a and interval of θ to graph the spiral in the window specified.
-$a=3,0 \leq \theta \leq 2 \pi,[-20,20] \text { by }[-20,20]$

Accepted Answer

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

Question 16

Draw a sketch to represent the vector. Refer to the vectors pictured here.  
-d - a

Accepted Answer

A)   
B)   
A)   
B)

Question 17

Find all specified roots.
-Cube roots of 1 .

Accepted Answer

A)  $1 , \frac { 1 } { 2 } - \frac { \sqrt { 3 } } { 2 } \mathrm { i } , - \frac { 1 } { 2 } - \frac { \sqrt { 3 } } { 2 } \mathrm { i }$ 
B)  $1 , \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } \mathrm { i } , - \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } \mathrm { i }$ 
C)  $- 1,1$ 
D)  $1 , - \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } \mathrm { i } , - \frac { 1 } { 2 } - \frac { \sqrt { 3 } } { 2 } \mathrm { i }$ 
A)  $1 , \frac { 1 } { 2 } - \frac { \sqrt { 3 } } { 2 } \mathrm { i } , - \frac { 1 } { 2 } - \frac { \sqrt { 3 } } { 2 } \mathrm { i }$ 
B)  $1 , \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } \mathrm { i } , - \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } \mathrm { i }$ 
C)  $- 1,1$ 
D)  $1 , - \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } \mathrm { i } , - \frac { 1 } { 2 } - \frac { \sqrt { 3 } } { 2 } \mathrm { i }$

Question 18

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form.
-$\frac { 16 \operatorname { cis } 337 ^ { \circ } } { 4 \operatorname { cis } 67 ^ { \circ } }$

Accepted Answer

A)  - $2 \mathrm { i }$ 
B)  $- 4$ 
C)  $- 4 \mathrm { i }$ 
D)  $- 2 \sqrt { 3 } + 2 i$ 
A)  - $2 \mathrm { i }$ 
B)  $- 4$ 
C)  $- 4 \mathrm { i }$ 
D)  $- 2 \sqrt { 3 } + 2 i$

Question 19

Find all cube roots of the complex number. Leave answers in trigonometric form.
-$- 27$

Accepted Answer

A)  $3 \operatorname { cis } 30 ^ { \circ } , 3 \operatorname { cis } 150 ^ { \circ } , 3 \operatorname { cis } 270 ^ { \circ }$ 
B)  $3 \operatorname { cis } 60 ^ { \circ } , 3$ cis $180 ^ { \circ } , 3$ cis $300 ^ { \circ }$ 
C)  $3 \operatorname { cis } 180 ^ { \circ } , 3 \operatorname { cis } 0 ^ { \circ }$ 
D)  $3 \operatorname { cis } 120 ^ { \circ } , 3 \operatorname { cis } 180 ^ { \circ } , 3 \operatorname { cis } 300 ^ { \circ }$ 
A)  $3 \operatorname { cis } 30 ^ { \circ } , 3 \operatorname { cis } 150 ^ { \circ } , 3 \operatorname { cis } 270 ^ { \circ }$ 
B)  $3 \operatorname { cis } 60 ^ { \circ } , 3$ cis $180 ^ { \circ } , 3$ cis $300 ^ { \circ }$ 
C)  $3 \operatorname { cis } 180 ^ { \circ } , 3 \operatorname { cis } 0 ^ { \circ }$ 
D)  $3 \operatorname { cis } 120 ^ { \circ } , 3 \operatorname { cis } 180 ^ { \circ } , 3 \operatorname { cis } 300 ^ { \circ }$

Question 20

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.
-$$\begin{array} { l } 
a = 153 \mathrm {~m} \
\mathrm {~b} = 165 \mathrm {~m} \
\mathrm { c } = 171 \mathrm {~m}
\end{array}$$

Accepted Answer

A)  $17,150 \mathrm {~m} ^ { 2 }$ 
B)  $14,291 \mathrm {~m} ^ { 2 }$ 
C)  $11,433 \mathrm {~m} ^ { 2 }$ 
D)  $731 \mathrm {~m} ^ { 2 }$ 
A)  $17,150 \mathrm {~m} ^ { 2 }$ 
B)  $14,291 \mathrm {~m} ^ { 2 }$ 
C)  $11,433 \mathrm {~m} ^ { 2 }$ 
D)  $731 \mathrm {~m} ^ { 2 }$

Write the complex number in rectangular form. -5.62( $\left. \cos 20 ^ { \circ } + i \sin 20 ^ { \circ } \right)$

Find sum of the pair of complex numbers. - $5 + 4 \mathrm { i } , 6$

Determine two pairs of polar coordinates for the point with 0° ≤ θ < 360°. - $( 3,3 )$

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations. - $x = \sin t , y = \cos t ; t = \pi$

Find the angle between the pair of vectors to the nearest tenth of a degree. - $\langle - 5 , - 7 \rangle , \langle 6 , - 4 \rangle$

Solve the problem. -Two boats are pulling a disabled vessel toward the landing dock with forces of $930 \mathrm { lb }$ and $890 \mathrm { lb }$ . The angle between the forces is $28.6 ^ { \circ }$ . Find the direction and magnitude of the equilibrant.

Plot the point. - $\left( - 4 , \frac { - 5 \pi } { 4 } \right)$ $Plot the point. - \left( - 4 , \frac { - 5 \pi } { 4 } \right)$

The graph of a polar equation is given. Select the polar equation for the graph. -

Find a rectangular equation for the plane curve defined by the parametric equations. - $x = t ^ { 2 } + 1 , y = t ^ { 2 } - 1$

Plot the point. - $\left( 4 , \frac { - 3 \pi } { 4 } \right)$ $Plot the point. - \left( 4 , \frac { - 3 \pi } { 4 } \right)$

Graph the polar equation for θ in [0°, 360°). - $r = 7 + 7 \sin \theta$ $Graph the polar equation for θ in [0°, 360°). - r = 7 + 7 \sin \theta$

Find the dot product for the pair of vectors. - $\langle 3,0 \rangle , \langle 18 , - 2 \rangle$

Solve the problem. -Two ships leave a harbor together traveling on courses that have an angle of $123 ^ { \circ }$ between them. they each travel 506 miles, how far apart are they (to the nearest mile)?

Find the missing parts of the triangle. - =65. =2.15 =2.25 If necessary, round angles to the nearest tenth and side lengths to the nearest hundredth.

The graph of r = aθ in polar coordinates is an example of the spiral of Archimedes. With your calculator set to radian mode, use the given value of a and interval of θ to graph the spiral in the window specified. - $a=3,0 \leq \theta \leq 2 \pi,[-20,20] \text { by }[-20,20]$

Draw a sketch to represent the vector. Refer to the vectors pictured here. -d - a

Find all specified roots. -Cube roots of 1 .

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - $\frac { 16 \operatorname { cis } 337 ^ { \circ } } { 4 \operatorname { cis } 67 ^ { \circ } }$

Find all cube roots of the complex number. Leave answers in trigonometric form. - $- 27$

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary. - a=153 =165 =171

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

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Exam 8: Applications of Trigonometry

Write the complex number in rectangular form. -5.62( cos⁡20∘+isin⁡20∘)\left. \cos 20 ^ { \circ } + i \sin 20 ^ { \circ } \right)cos20∘+isin20∘)

Find sum of the pair of complex numbers. - 5+4i,65 + 4 \mathrm { i } , 65+4i,6

Determine two pairs of polar coordinates for the point with 0° ≤ θ < 360°. - (3,3)( 3,3 )(3,3)

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations. - x=sin⁡t,y=cos⁡t;t=πx = \sin t , y = \cos t ; t = \pix=sint,y=cost;t=π

Find the angle between the pair of vectors to the nearest tenth of a degree. - ⟨−5,−7⟩,⟨6,−4⟩\langle - 5 , - 7 \rangle , \langle 6 , - 4 \rangle⟨−5,−7⟩,⟨6,−4⟩

Solve the problem. -Two boats are pulling a disabled vessel toward the landing dock with forces of 930lb930 \mathrm { lb }930lb and 890lb890 \mathrm { lb }890lb . The angle between the forces is 28.6∘28.6 ^ { \circ }28.6∘ . Find the direction and magnitude of the equilibrant.

Plot the point. - (−4,−5π4)\left( - 4 , \frac { - 5 \pi } { 4 } \right)(−4,4−5π​)

The graph of a polar equation is given. Select the polar equation for the graph. -

Find a rectangular equation for the plane curve defined by the parametric equations. - x=t2+1,y=t2−1x = t ^ { 2 } + 1 , y = t ^ { 2 } - 1x=t2+1,y=t2−1

Plot the point. - (4,−3π4)\left( 4 , \frac { - 3 \pi } { 4 } \right)(4,4−3π​)

Graph the polar equation for θ in [0°, 360°). - r=7+7sin⁡θr = 7 + 7 \sin \thetar=7+7sinθ

Find the dot product for the pair of vectors. - ⟨3,0⟩,⟨18,−2⟩\langle 3,0 \rangle , \langle 18 , - 2 \rangle⟨3,0⟩,⟨18,−2⟩

Solve the problem. -Two ships leave a harbor together traveling on courses that have an angle of 123∘123 ^ { \circ }123∘ between them. they each travel 506 miles, how far apart are they (to the nearest mile)?

Find the missing parts of the triangle. - =65. =2.15 =2.25 If necessary, round angles to the nearest tenth and side lengths to the nearest hundredth.

Draw a sketch to represent the vector. Refer to the vectors pictured here. -d - a

Find all specified roots. -Cube roots of 1 .

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - 16cis⁡337∘4cis⁡67∘\frac { 16 \operatorname { cis } 337 ^ { \circ } } { 4 \operatorname { cis } 67 ^ { \circ } }4cis67∘16cis337∘​

Find all cube roots of the complex number. Leave answers in trigonometric form. - −27- 27−27

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary. - a=153 =165 =171

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Write the complex number in rectangular form. -5.62( $\left. \cos 20 ^ { \circ } + i \sin 20 ^ { \circ } \right)$

Find sum of the pair of complex numbers. - $5 + 4 \mathrm { i } , 6$

Determine two pairs of polar coordinates for the point with 0° ≤ θ < 360°. - $( 3,3 )$

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations. - $x = \sin t , y = \cos t ; t = \pi$

Find the angle between the pair of vectors to the nearest tenth of a degree. - $\langle - 5 , - 7 \rangle , \langle 6 , - 4 \rangle$

Solve the problem. -Two boats are pulling a disabled vessel toward the landing dock with forces of $930 \mathrm { lb }$ and $890 \mathrm { lb }$ . The angle between the forces is $28.6 ^ { \circ }$ . Find the direction and magnitude of the equilibrant.

Plot the point. - $\left( - 4 , \frac { - 5 \pi } { 4 } \right)$ $Plot the point. - \left( - 4 , \frac { - 5 \pi } { 4 } \right)$

Find a rectangular equation for the plane curve defined by the parametric equations. - $x = t ^ { 2 } + 1 , y = t ^ { 2 } - 1$

Plot the point. - $\left( 4 , \frac { - 3 \pi } { 4 } \right)$ $Plot the point. - \left( 4 , \frac { - 3 \pi } { 4 } \right)$

Graph the polar equation for θ in [0°, 360°). - $r = 7 + 7 \sin \theta$ $Graph the polar equation for θ in [0°, 360°). - r = 7 + 7 \sin \theta$

Find the dot product for the pair of vectors. - $\langle 3,0 \rangle , \langle 18 , - 2 \rangle$

Solve the problem. -Two ships leave a harbor together traveling on courses that have an angle of $123 ^ { \circ }$ between them. they each travel 506 miles, how far apart are they (to the nearest mile)?

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - $\frac { 16 \operatorname { cis } 337 ^ { \circ } } { 4 \operatorname { cis } 67 ^ { \circ } }$

Find all cube roots of the complex number. Leave answers in trigonometric form. - $- 27$