Question 1

Graph the polar equation for θ in [0°, 360°).
-$$r = 5 \sin 3 \theta$$

Accepted Answer

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

Question 2

Find the product. Write the product in rectangular form, using exact values.
-$\left[ 8 \operatorname { cis } 240 ^ { \circ } \right] \left[ 6 \operatorname { cis } 330 ^ { \circ } \right]$

Accepted Answer

A)  $- 24 \sqrt { 3 } - 24 \mathrm { i }$ 
B)  $- 12 + 12 \sqrt { 3 } i$ 
C)  $24 \mathrm { i }$ 
D)  24 
A)  $- 24 \sqrt { 3 } - 24 \mathrm { i }$ 
B)  $- 12 + 12 \sqrt { 3 } i$ 
C)  $24 \mathrm { i }$ 
D)  24

Question 3

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
-Why canʹt the Pythagorean theorem be used to solve an oblique triangle?

Accepted Answer

The Pythagorean theo

Question 4

Use a table of values to graph the plane curve defined by the following parametric equations. Find a rectangular
equation for the curve.
-

Accepted Answer

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

Question 5

The rectangular coordinates of a point are given. Express the point in polar coordinates with r ≥ 0 and 0° ≤ θ < 360°.
-$( 0 , \sqrt { 7 } )$

Accepted Answer

A)  $\left( 7,90 ^ { \circ } \right)$ 
B)  $\left( \sqrt { 7 } , 270 ^ { \circ } \right)$ 
C)  $\left( 7,270 ^ { \circ } \right)$ 
D)  $\left( \sqrt { 7 } , 90 ^ { \circ } \right)$ 
A)  $\left( 7,90 ^ { \circ } \right)$ 
B)  $\left( \sqrt { 7 } , 270 ^ { \circ } \right)$ 
C)  $\left( 7,270 ^ { \circ } \right)$ 
D)  $\left( \sqrt { 7 } , 90 ^ { \circ } \right)$

Question 6

Determine whether the pair of vectors is orthogonal.
-$$\langle 8 , - 2 \rangle , \langle - 3 , - 4 \rangle$$

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 7

Find all specified roots.
-Eleventh roots of 1 .

Accepted Answer

A)  $1 , \operatorname { cis } \frac { 2 \pi } { 11 } , \operatorname { cis } \frac { 4 \pi } { 11 } , \operatorname { cis } \frac { 6 \pi } { 11 } , \operatorname { cis } \frac { 8 \pi } { 11 } , \operatorname { cis } \frac { 10 \pi } { 11 } , \operatorname { cis } \frac { 12 \pi } { 11 } , \operatorname { cis } \frac { 14 \pi } { 11 } , \operatorname { cis } \frac { 16 \pi } { 11 } , \operatorname { cis } \frac { 18 \pi } { 11 } , - 1$ 
B)  $1 , \operatorname { cis } \frac { 2 \pi } { 11 } , \operatorname { cis } \frac { 4 \pi } { 11 } , \operatorname { cis } \frac { 6 \pi } { 11 } , \operatorname { cis } \frac { 8 \pi } { 11 } , \operatorname { cis } \frac { 10 \pi } { 11 } , \operatorname { cis } \frac { 12 \pi } { 11 } , \operatorname { cis } \frac { 14 \pi } { 11 } , \operatorname { cis } \frac { 16 \pi } { 11 } , \operatorname { cis } \frac { 18 \pi } { 11 } , \operatorname { cis } \frac { 20 \pi } { 11 }$ 
C) 
 $1 , \operatorname { cis } \frac { 2 \pi } { 11 } , \operatorname { cis } \frac { 4 \pi } { 11 } , \operatorname { cis } \frac { 6 \pi } { 11 } , \operatorname { cis } \frac { 8 \pi } { 11 } , \operatorname { cis } \frac { 10 \pi } { 11 }$ 
D)  $1 , \operatorname { cis } \frac { \pi } { 11 } , \operatorname { cis } \frac { 2 \pi } { 11 } , \operatorname { cis } \frac { 3 \pi } { 11 } , \operatorname { cis } \frac { 4 \pi } { 11 } , \operatorname { cis } \frac { 5 \pi } { 11 } , \operatorname { cis } \frac { 6 \pi } { 11 } , \operatorname { cis } \frac { 7 \pi } { 11 } , \operatorname { cis } \frac { 8 \pi } { 11 } , \operatorname { cis } \frac { 9 \pi } { 11 } , \operatorname { cis } \frac { 10 \pi } { 11 }$ 
A)  $1 , \operatorname { cis } \frac { 2 \pi } { 11 } , \operatorname { cis } \frac { 4 \pi } { 11 } , \operatorname { cis } \frac { 6 \pi } { 11 } , \operatorname { cis } \frac { 8 \pi } { 11 } , \operatorname { cis } \frac { 10 \pi } { 11 } , \operatorname { cis } \frac { 12 \pi } { 11 } , \operatorname { cis } \frac { 14 \pi } { 11 } , \operatorname { cis } \frac { 16 \pi } { 11 } , \operatorname { cis } \frac { 18 \pi } { 11 } , - 1$ 
B)  $1 , \operatorname { cis } \frac { 2 \pi } { 11 } , \operatorname { cis } \frac { 4 \pi } { 11 } , \operatorname { cis } \frac { 6 \pi } { 11 } , \operatorname { cis } \frac { 8 \pi } { 11 } , \operatorname { cis } \frac { 10 \pi } { 11 } , \operatorname { cis } \frac { 12 \pi } { 11 } , \operatorname { cis } \frac { 14 \pi } { 11 } , \operatorname { cis } \frac { 16 \pi } { 11 } , \operatorname { cis } \frac { 18 \pi } { 11 } , \operatorname { cis } \frac { 20 \pi } { 11 }$ 
C) 
 $1 , \operatorname { cis } \frac { 2 \pi } { 11 } , \operatorname { cis } \frac { 4 \pi } { 11 } , \operatorname { cis } \frac { 6 \pi } { 11 } , \operatorname { cis } \frac { 8 \pi } { 11 } , \operatorname { cis } \frac { 10 \pi } { 11 }$ 
D)  $1 , \operatorname { cis } \frac { \pi } { 11 } , \operatorname { cis } \frac { 2 \pi } { 11 } , \operatorname { cis } \frac { 3 \pi } { 11 } , \operatorname { cis } \frac { 4 \pi } { 11 } , \operatorname { cis } \frac { 5 \pi } { 11 } , \operatorname { cis } \frac { 6 \pi } { 11 } , \operatorname { cis } \frac { 7 \pi } { 11 } , \operatorname { cis } \frac { 8 \pi } { 11 } , \operatorname { cis } \frac { 9 \pi } { 11 } , \operatorname { cis } \frac { 10 \pi } { 11 }$

Question 8

Solve.
-A complex number $z$ does not belong to the Mandelbrot set if any of the complex numbers in the sequence $z , z ^ { 2 } + z , \left( z ^ { 2 } + z \right) ^ { 2 } + z , \left[ \left( z ^ { 2 } + z \right) ^ { 2 } + z \right] ^ { 2 } + z , \ldots$ has modulus exceeding 2. Does $z = - 1.4 i$ belong to the Mandelbrot set?

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 9

Find the missing parts of the triangle.
-$$\begin{array} { l } 
\mathrm { B } = 40.1 ^ { \circ } \
\mathrm { b } = 24.1 \mathrm { in } . \
\mathrm { c } = 19.4 \mathrm { in } .
\end{array}$$
If necessary, round angles and side lengths to the nearest tenth.

Accepted Answer

A)  $\mathrm { A } = 108.7 ^ { \circ } , \mathrm { C } = 31.2 ^ { \circ } , \mathrm { a } = 35.4 \mathrm { in }$. 
B)  no such triangle 
C)  $\mathrm { A } = 31.2 ^ { \circ } , \mathrm { C } = 108.7 ^ { \circ } , \mathrm { a } = 35.4 \mathrm { in }$. 
D)  $\mathrm { A } = 98.7 ^ { \circ } , \mathrm { C } = 41.2 ^ { \circ } , \mathrm { a } = 35.4 \mathrm { in }$. 
A)  $\mathrm { A } = 108.7 ^ { \circ } , \mathrm { C } = 31.2 ^ { \circ } , \mathrm { a } = 35.4 \mathrm { in }$. 
B)  no such triangle 
C)  $\mathrm { A } = 31.2 ^ { \circ } , \mathrm { C } = 108.7 ^ { \circ } , \mathrm { a } = 35.4 \mathrm { in }$. 
D)  $\mathrm { A } = 98.7 ^ { \circ } , \mathrm { C } = 41.2 ^ { \circ } , \mathrm { a } = 35.4 \mathrm { in }$.

Question 10

Is the given number z in the Julia set?
-$$z = 1.5 - 0 \mathrm { i }$$

Accepted Answer

A)  Yes 
B)  $\mathrm { No }$ 
A)  Yes 
B)  $\mathrm { No }$

Question 11

Find all solutions of the equation. Leave answers in trigonometric form.
-$$x ^ { 3 } + 8 i = 0$$

Accepted Answer

A)  $\left\{ 2 \operatorname { cis } 270 ^ { \circ } , 2 \operatorname { cis } 210 ^ { \circ } , 2 \right.$ cis $\left. 150 ^ { \circ } \right\}$ 
B)  $\left\{ 2 \operatorname { cis } 90 ^ { \circ } , 2 \operatorname { cis } 150 ^ { \circ } , 2 \operatorname { cis } 30 ^ { \circ } \right\}$ 
C)  $\left\{ 2 \operatorname { cis } 90 ^ { \circ } , 2 \operatorname { cis } 210 ^ { \circ } , 2 \operatorname { cis } 330 ^ { \circ } \right\}$ 
D)  $\left\{ 2 \operatorname { cis } 270 ^ { \circ } , 2 \operatorname { cis } 30 ^ { \circ } , 2 \operatorname { cis } 150 ^ { \circ } \right\}$ 
A)  $\left\{ 2 \operatorname { cis } 270 ^ { \circ } , 2 \operatorname { cis } 210 ^ { \circ } , 2 \right.$ cis $\left. 150 ^ { \circ } \right\}$ 
B)  $\left\{ 2 \operatorname { cis } 90 ^ { \circ } , 2 \operatorname { cis } 150 ^ { \circ } , 2 \operatorname { cis } 30 ^ { \circ } \right\}$ 
C)  $\left\{ 2 \operatorname { cis } 90 ^ { \circ } , 2 \operatorname { cis } 210 ^ { \circ } , 2 \operatorname { cis } 330 ^ { \circ } \right\}$ 
D)  $\left\{ 2 \operatorname { cis } 270 ^ { \circ } , 2 \operatorname { cis } 30 ^ { \circ } , 2 \operatorname { cis } 150 ^ { \circ } \right\}$

Question 12

Solve the problem.
-Lookout station B is located 6 mi due east of station A. The bearing of a fire from A is $\mathrm { S } 9 ^ { \circ } 50 ^ { \prime } \mathrm { W }$ and the bearing from B is $S 28 ^ { \circ } 50 ^ { \prime } W$. Determine the distance from the fire to B (to the nearest tenth of a mile).

Accepted Answer

A)  $9.1 \mathrm { mi }$ 
B)  $11.1 \mathrm { mi }$ 
C)  $18.2 \mathrm { mi }$ 
D)  $20.2 \mathrm { mi }$ 
A)  $9.1 \mathrm { mi }$ 
B)  $11.1 \mathrm { mi }$ 
C)  $18.2 \mathrm { mi }$ 
D)  $20.2 \mathrm { mi }$

Question 13

Solve the problem.
-The sides of a parallelogram are $15 \mathrm { ft }$ and $17 \mathrm { ft }$. One angle is $44 ^ { \circ }$ while another angle is $136 ^ { \circ }$. Find the lengths of the diagonals of the parallelogram (to the nearest tenth of a foot).

Accepted Answer

A)  $18.2 \mathrm { ft }$ and $26.4 \mathrm { ft }$ 
B)  $20 \mathrm { ft }$ and $12.1 \mathrm { ft }$ 
C)  $147.1 \mathrm { ft }$ and $880.9 \mathrm { ft }$ 
D)  $12.1 \mathrm { ft }$ and $29.7 \mathrm { ft }$ 
A)  $18.2 \mathrm { ft }$ and $26.4 \mathrm { ft }$ 
B)  $20 \mathrm { ft }$ and $12.1 \mathrm { ft }$ 
C)  $147.1 \mathrm { ft }$ and $880.9 \mathrm { ft }$ 
D)  $12.1 \mathrm { ft }$ and $29.7 \mathrm { ft }$

Question 14

Solve the problem.
-To find the distance $\mathrm { AB }$ across a river, a distance $\mathrm { BC } = 658 \mathrm {~m}$ is laid off on one side of the river. It is found that $\mathrm { B } = 114.8 ^ { \circ }$ and $\mathrm { C } = 14.6 ^ { \circ }$. Find $\mathrm { AB }$ rounded to the nearest meter.

Accepted Answer

A)  $218 \mathrm {~m}$ 
B)  $215 \mathrm {~m}$ 
C)  $166 \mathrm {~m}$ 
D)  $169 \mathrm {~m}$ 
A)  $218 \mathrm {~m}$ 
B)  $215 \mathrm {~m}$ 
C)  $166 \mathrm {~m}$ 
D)  $169 \mathrm {~m}$

Question 15

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides,
by the law of sines.
-C, c, and A

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 16

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

Accepted Answer

A)  $r = 8 \cos \theta$ 
B)  $\mathrm { r } = 4 + \cos \theta$ 
C)  $r = 4 + \sin \theta$ 
D)  $r = 8 \sin \theta$ 
A)  $r = 8 \cos \theta$ 
B)  $\mathrm { r } = 4 + \cos \theta$ 
C)  $r = 4 + \sin \theta$ 
D)  $r = 8 \sin \theta$

Question 17

Solve the problem.
-Given that the polar equation $\mathrm { r } = \frac { \mathrm { a } \left( 1 - \mathrm { e } ^ { 2 } \right) } { 1 + \mathrm { e } \cos \theta }$ models the orbits of the planets, estimate the closest approach of Pluto's orbit, for which $\mathrm { a } = 39.4$ and $\mathrm { e } = 0.249$, to the sun.

Accepted Answer

A)  About 50 astronomical units 
B)  About 74 astronomical units 
C)  About 39 astronomical units 
D)  About 30 astronomical units 
A)  About 50 astronomical units 
B)  About 74 astronomical units 
C)  About 39 astronomical units 
D)  About 30 astronomical units

Question 18

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides,
by the law of sines.
-a, c, and C

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 19

Solve the problem.
-Suppose that a radio transmission pattern can be modeled by $r ^ { 2 } = 3600 \cos 2 \theta$, for $0 ^ { \circ } \leq \theta \leq 360 ^ { \circ }$, where the units are miles. Determine how far the signal reaches to the east, assuming that east is represented by the direction of the positive $x$-axis.

Accepted Answer

A)  3600 miles 
B)  7200 miles 
C)  60 miles 
D)  120 miles 
A)  3600 miles 
B)  7200 miles 
C)  60 miles 
D)  120 miles

Question 20

Solve the problem.
-A guy wire to a tower makes a $71 ^ { \circ }$ angle with level ground. At a point $32 \mathrm { ft }$ farther from the tower than the wire but on the same side of the base as the wire, the angle of elevation to the top of the pole is $34 ^ { \circ }$. Find the wire length (to the nearest foot).

Accepted Answer

A)  $65 \mathrm { ft }$ 
B)  $30 \mathrm { ft }$ 
C)  $60 \mathrm { ft }$ 
D)  $35 \mathrm { ft }$ 
A)  $65 \mathrm { ft }$ 
B)  $30 \mathrm { ft }$ 
C)  $60 \mathrm { ft }$ 
D)  $35 \mathrm { ft }$

Graph the polar equation for θ in [0°, 360°). - $r = 5 \sin 3 \theta$ $Graph the polar equation for θ in [0°, 360°). - r = 5 \sin 3 \theta$

Find the product. Write the product in rectangular form, using exact values. - $\left[ 8 \operatorname { cis } 240 ^ { \circ } \right] \left[ 6 \operatorname { cis } 330 ^ { \circ } \right]$

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Why canʹt the Pythagorean theorem be used to solve an oblique triangle?

Use a table of values to graph the plane curve defined by the following parametric equations. Find a rectangular equation for the curve. -

The rectangular coordinates of a point are given. Express the point in polar coordinates with r ≥ 0 and 0° ≤ θ < 360°. - $( 0 , \sqrt { 7 } )$

Determine whether the pair of vectors is orthogonal. - $\langle 8 , - 2 \rangle , \langle - 3 , - 4 \rangle$

Find all specified roots. -Eleventh roots of 1 .

Find the missing parts of the triangle. - =40. =24.1. =19.4. If necessary, round angles and side lengths to the nearest tenth.

Is the given number z in the Julia set? - $z = 1.5 - 0 \mathrm { i }$

Find all solutions of the equation. Leave answers in trigonometric form. - $x ^ { 3 } + 8 i = 0$

Solve the problem. -The sides of a parallelogram are $15 \mathrm { ft }$ and $17 \mathrm { ft }$ . One angle is $44 ^ { \circ }$ while another angle is $136 ^ { \circ }$ . Find the lengths of the diagonals of the parallelogram (to the nearest tenth of a foot).

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides, by the law of sines. -C, c, and A

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

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides, by the law of sines. -a, c, and C

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

Exam 8: Applications of Trigonometry

Graph the polar equation for θ in [0°, 360°). - r=5sin⁡3θr = 5 \sin 3 \thetar=5sin3θ

Find the product. Write the product in rectangular form, using exact values. - [8cis⁡240∘][6cis⁡330∘]\left[ 8 \operatorname { cis } 240 ^ { \circ } \right] \left[ 6 \operatorname { cis } 330 ^ { \circ } \right][8cis240∘][6cis330∘]

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Why canʹt the Pythagorean theorem be used to solve an oblique triangle?

Use a table of values to graph the plane curve defined by the following parametric equations. Find a rectangular equation for the curve. -

The rectangular coordinates of a point are given. Express the point in polar coordinates with r ≥ 0 and 0° ≤ θ < 360°. - (0,7)( 0 , \sqrt { 7 } )(0,7​)

Determine whether the pair of vectors is orthogonal. - ⟨8,−2⟩,⟨−3,−4⟩\langle 8 , - 2 \rangle , \langle - 3 , - 4 \rangle⟨8,−2⟩,⟨−3,−4⟩

Find all specified roots. -Eleventh roots of 1 .

Find the missing parts of the triangle. - =40. =24.1. =19.4. If necessary, round angles and side lengths to the nearest tenth.

Is the given number z in the Julia set? - z=1.5−0iz = 1.5 - 0 \mathrm { i }z=1.5−0i

Find all solutions of the equation. Leave answers in trigonometric form. - x3+8i=0x ^ { 3 } + 8 i = 0x3+8i=0

Solve the problem. -The sides of a parallelogram are 15ft15 \mathrm { ft }15ft and 17ft17 \mathrm { ft }17ft . One angle is 44∘44 ^ { \circ }44∘ while another angle is 136∘136 ^ { \circ }136∘ . Find the lengths of the diagonals of the parallelogram (to the nearest tenth of a foot).

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides, by the law of sines. -C, c, and A

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

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides, by the law of sines. -a, c, and C

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

Graph the polar equation for θ in [0°, 360°). - $r = 5 \sin 3 \theta$ $Graph the polar equation for θ in [0°, 360°). - r = 5 \sin 3 \theta$

Find the product. Write the product in rectangular form, using exact values. - $\left[ 8 \operatorname { cis } 240 ^ { \circ } \right] \left[ 6 \operatorname { cis } 330 ^ { \circ } \right]$

The rectangular coordinates of a point are given. Express the point in polar coordinates with r ≥ 0 and 0° ≤ θ < 360°. - $( 0 , \sqrt { 7 } )$

Determine whether the pair of vectors is orthogonal. - $\langle 8 , - 2 \rangle , \langle - 3 , - 4 \rangle$

Is the given number z in the Julia set? - $z = 1.5 - 0 \mathrm { i }$

Find all solutions of the equation. Leave answers in trigonometric form. - $x ^ { 3 } + 8 i = 0$

Solve the problem. -The sides of a parallelogram are $15 \mathrm { ft }$ and $17 \mathrm { ft }$ . One angle is $44 ^ { \circ }$ while another angle is $136 ^ { \circ }$ . Find the lengths of the diagonals of the parallelogram (to the nearest tenth of a foot).