Question 1

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

Accepted Answer

A) 
  
B) 
  
A) 
  
B)

Question 2

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.
-$$\begin{array} { l } 
a = 150 \mathrm {~m} \
\mathrm {~b} = 164 \mathrm {~m} \
\mathrm { c } = 172 \mathrm {~m}
\end{array}$$

Accepted Answer

A)  $16,889 \mathrm {~m} ^ { 2 }$ 
B)  $14,074 \mathrm {~m} ^ { 2 }$ 
C)  $11,259 \mathrm {~m} ^ { 2 }$ 
D)  $722 \mathrm {~m} ^ { 2 }$ 
A)  $16,889 \mathrm {~m} ^ { 2 }$ 
B)  $14,074 \mathrm {~m} ^ { 2 }$ 
C)  $11,259 \mathrm {~m} ^ { 2 }$ 
D)  $722 \mathrm {~m} ^ { 2 }$

Question 3

Find all cube roots of the complex number. Leave answers in trigonometric form.
-$- 125 \mathrm { i }$

Accepted Answer

A)  $5 \operatorname { cis } ^ { \circ } 210,5 \operatorname { cis } 270 ^ { \circ } , 5 \operatorname { cis } 330 ^ { \circ }$ 
B)  $5 \operatorname { cis } 30 ^ { \circ } , 5 \operatorname { cis } ^ { \circ } 60,5 \operatorname { cis } 90 ^ { \circ }$ 
C)  $5 \operatorname { cis } 90 ^ { \circ } , 5 \operatorname { cis } ^ { \circ } 180,5 \operatorname { cis } 270 ^ { \circ }$ 
D)  $5 \operatorname { cis } 90 ^ { \circ } , 5 \operatorname { cis } ^ { \circ } 210,5 \operatorname { cis } 330 ^ { \circ }$ 
A)  $5 \operatorname { cis } ^ { \circ } 210,5 \operatorname { cis } 270 ^ { \circ } , 5 \operatorname { cis } 330 ^ { \circ }$ 
B)  $5 \operatorname { cis } 30 ^ { \circ } , 5 \operatorname { cis } ^ { \circ } 60,5 \operatorname { cis } 90 ^ { \circ }$ 
C)  $5 \operatorname { cis } 90 ^ { \circ } , 5 \operatorname { cis } ^ { \circ } 180,5 \operatorname { cis } 270 ^ { \circ }$ 
D)  $5 \operatorname { cis } 90 ^ { \circ } , 5 \operatorname { cis } ^ { \circ } 210,5 \operatorname { cis } 330 ^ { \circ }$

Question 4

Solve.
-A complex number $\mathrm { z }$ 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 $\mathrm { z } = 0.5 - 0.4 \mathrm { i }$ belong to the Mandelbrot set?

Accepted Answer

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

Question 5

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form.
-$$\frac { 16 \left( \cos 240 ^ { \circ } + i \sin 240 ^ { \circ } \right) } { 4 \left( \cos 60 ^ { \circ } + i \sin 60 ^ { \circ } \right) }$$

Accepted Answer

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

Question 6

Solve the problem.
-A ship sailing parallel to shore sights a lighthouse at an angle of $14 ^ { \circ }$ from its direction of travel. After traveling 4 miles farther, the angle is $24 ^ { \circ }$. At that time, how far is the ship from the lighthouse? If necessary, round to the nearest hundredth of a mile.

Accepted Answer

A)  $2.38 \mathrm { mi }$ 
B)  $9.37 \mathrm { mi }$ 
C)  $5.57 \mathrm { mi }$ 
D)  $4 \mathrm { mi }$ 
A)  $2.38 \mathrm { mi }$ 
B)  $9.37 \mathrm { mi }$ 
C)  $5.57 \mathrm { mi }$ 
D)  $4 \mathrm { mi }$

Question 7

Write the vector in the form <a, b>. If necessary, round values to the nearest hundredth.
-

Accepted Answer

A)  $\langle - 15.84 , - 46 \rangle$ 
B)  $\langle - 14.98 , - 43.49 \rangle$ 
C)  $\langle - 43.49 , - 14.98 \rangle$ 
D)  $\langle - 0.33 , - 0.95 \rangle$ 
A)  $\langle - 15.84 , - 46 \rangle$ 
B)  $\langle - 14.98 , - 43.49 \rangle$ 
C)  $\langle - 43.49 , - 14.98 \rangle$ 
D)  $\langle - 0.33 , - 0.95 \rangle$

Question 8

Provide an appropriate response.
-The parametric equations $$x = 2 \tan t , y = 3 \sec t$$ will graph a parabola.

Accepted Answer

A) True 
 B)False

Question 9

Find the component form of the indicated vector.
-Let $\mathbf { u } = \langle 3,1 \rangle , \mathbf { v } = \langle 4 , - 5 \rangle$. Find $2 \mathbf { u } + 3 \mathbf { v }$.

Accepted Answer

A)  $\langle 14 , - 8 \rangle$ 
B)  $\langle - 6,17 \rangle$ 
C)  $\langle 18 , - 4 \rangle$ 
D)  $\langle 18 , - 13 \rangle$ 
A)  $\langle 14 , - 8 \rangle$ 
B)  $\langle - 6,17 \rangle$ 
C)  $\langle 18 , - 4 \rangle$ 
D)  $\langle 18 , - 13 \rangle$

Question 10

Determine the number of triangles ABC possible with the given parts.
-$$a = 15 , b = 26 , B = 98 ^ { \circ }$$

Accepted Answer

A)  0 
B)  3 
C)  1 
D)  2 
A)  0 
B)  3 
C)  1 
D)  2

Question 11

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as
an angle in $$\left[ 0,360 ^ { \circ } \right]$$
-4, 4

Accepted Answer

A)  $4 ; 225 ^ { \circ }$ 
B)  $8 ; 45 ^ { \circ }$ 
C)  $4 \sqrt { 2 } ; 45 ^ { \circ }$ 
D)  $4 \sqrt { 2 } ; 225 ^ { \circ }$ 
A)  $4 ; 225 ^ { \circ }$ 
B)  $8 ; 45 ^ { \circ }$ 
C)  $4 \sqrt { 2 } ; 45 ^ { \circ }$ 
D)  $4 \sqrt { 2 } ; 225 ^ { \circ }$

Question 12

Find the given power. Write answer in rectangular form.
-$$\left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right) ^{12}$$

Accepted Answer

A)  1 
B)  -i 
C)  i 
D)  -1 
A)  1 
B)  -i 
C)  i 
D)  -1

Question 13

Solve the problem.
-Points A and B are on opposite sides of a lake. Point $C$ is $101.0$ meters from $A$. The measure of angle BAC is $76 ^ { \circ } 30 ^ { \prime }$, and the measure of angle ACB is determined to be $39 ^ { \circ } 30 ^ { \prime }$. Find the distance between points $\mathrm { A }$ and $\mathrm { B }$ (to the nearest meter).

Accepted Answer

A)  $69 \mathrm {~m}$ 
B)  $34 \mathrm {~m}$ 
C)  $71 \mathrm {~m}$ 
D)  $36 \mathrm {~m}$ 
A)  $69 \mathrm {~m}$ 
B)  $34 \mathrm {~m}$ 
C)  $71 \mathrm {~m}$ 
D)  $36 \mathrm {~m}$

Question 14

Find the dot product for the pair of vectors.
--7j, 5i

Accepted Answer

A)  12 
B)  -2 
C)  -12 
D)  0 
A)  12 
B)  -2 
C)  -12 
D)  0

Question 15

Graph the cycloid for t in the indicated interval.
-$$\mathrm { x } = \mathrm { t } - \sin \mathrm { t } , \mathrm { y } = 1 - \cos \mathrm { t } , - 4 \pi \leq t \leq 4 \pi$$

Accepted Answer

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

Question 16

Find the missing parts of the triangle.
- 
If necessary, round angles to the nearest degree and give exact values of side lengths.

Accepted Answer

A)  $\mathrm { A } = 75 ^ { \circ } , \mathrm { C } = 45 ^ { \circ } , \mathrm { c } = 5 \sqrt { 3 } + 5$ 
B)  no such triangle 
C)  $\mathrm { A } = 45 ^ { \circ } , \mathrm { C } = 75 ^ { \circ } , \mathrm { c } = 5 \sqrt { 3 }$ 
D)  $\mathrm { A } = 45 ^ { \circ } , \mathrm { C } = 75 ^ { \circ } , \mathrm { c } = 5 \sqrt { 3 } + 5$ 
A)  $\mathrm { A } = 75 ^ { \circ } , \mathrm { C } = 45 ^ { \circ } , \mathrm { c } = 5 \sqrt { 3 } + 5$ 
B)  no such triangle 
C)  $\mathrm { A } = 45 ^ { \circ } , \mathrm { C } = 75 ^ { \circ } , \mathrm { c } = 5 \sqrt { 3 }$ 
D)  $\mathrm { A } = 45 ^ { \circ } , \mathrm { C } = 75 ^ { \circ } , \mathrm { c } = 5 \sqrt { 3 } + 5$

Question 17

Draw a sketch to represent the vector. Refer to the vectors pictured here.  
-$$a + ( c + d )$$

Accepted Answer

A) 
  
B) 
  
A) 
  
B)

Question 18

Find the product. Write the product in rectangular form, using exact values.
-$\left[ 3 \left( \cos 45 ^ { \circ } + i \sin 45 ^ { \circ } \right) \right] \left[ 2 \left( \cos 90 ^ { \circ } + i \sin 90 ^ { \circ } \right) \right]$

Accepted Answer

A)  $- 6 \sqrt { 2 } - 6 \sqrt { 2 } i$ 
B)  $3 \sqrt { 2 } - 12 \sqrt { 2 } \mathrm { i }$ 
C)  $2 \sqrt { 6 } - \sqrt { 2 } \mathrm { i }$ 
D)  $- 3 \sqrt { 2 } + 3 \sqrt { 2 } i$ 
A)  $- 6 \sqrt { 2 } - 6 \sqrt { 2 } i$ 
B)  $3 \sqrt { 2 } - 12 \sqrt { 2 } \mathrm { i }$ 
C)  $2 \sqrt { 6 } - \sqrt { 2 } \mathrm { i }$ 
D)  $- 3 \sqrt { 2 } + 3 \sqrt { 2 } i$

Question 19

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

Accepted Answer

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

Question 20

Write the complex number in rectangular form.
-$9 \left( \cos 180 ^ { \circ } + \mathrm { i } \sin 180 ^ { \circ } \right)$

Accepted Answer

A)  $9 \mathrm { i }$ 
B)  9 
C)  $- 9$ 
D)  $- 9 \mathrm { i }$ 
A)  $9 \mathrm { i }$ 
B)  9 
C)  $- 9$ 
D)  $- 9 \mathrm { i }$

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

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary. - a=150 =164 =172

Find all cube roots of the complex number. Leave answers in trigonometric form. - $- 125 \mathrm { i }$

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - $\frac { 16 \left( \cos 240 ^ { \circ } + i \sin 240 ^ { \circ } \right) } { 4 \left( \cos 60 ^ { \circ } + i \sin 60 ^ { \circ } \right) }$

Write the vector in the form <a, b>. If necessary, round values to the nearest hundredth. -

Provide an appropriate response. -The parametric equations $x = 2 \tan t , y = 3 \sec t$ will graph a parabola.

Find the component form of the indicated vector. -Let $\mathbf { u } = \langle 3,1 \rangle , \mathbf { v } = \langle 4 , - 5 \rangle$ . Find $2 \mathbf { u } + 3 \mathbf { v }$ .

Determine the number of triangles ABC possible with the given parts. - $a = 15 , b = 26 , B = 98 ^ { \circ }$

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in $\left[ 0,360 ^ { \circ } \right]$ -4, 4

Find the given power. Write answer in rectangular form. - $\left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right) ^{12}$

Find the dot product for the pair of vectors. --7j, 5i

Find the missing parts of the triangle. - If necessary, round angles to the nearest degree and give exact values of side lengths.

Draw a sketch to represent the vector. Refer to the vectors pictured here. - $a + ( c + d )$

Find the product. Write the product in rectangular form, using exact values. - $\left[ 3 \left( \cos 45 ^ { \circ } + i \sin 45 ^ { \circ } \right) \right] \left[ 2 \left( \cos 90 ^ { \circ } + i \sin 90 ^ { \circ } \right) \right]$

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

Write the complex number in rectangular form. - $9 \left( \cos 180 ^ { \circ } + \mathrm { i } \sin 180 ^ { \circ } \right)$

Review of Basic Concepts

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

Filters

Exam 9: Applications of Trigonometry