Question 1

Find the given power. Write answer in rectangular form.
-$$( - \sqrt { 3 } + i ) ^ { 6 }$$

Accepted Answer

A)  $64 - 64 \sqrt { 3 } i$ 
B)  $- 64$ 
C)  $- 64 \sqrt { 3 } + 64 i$ 
D)  $64 \mathrm { i }$ 
A)  $64 - 64 \sqrt { 3 } i$ 
B)  $- 64$ 
C)  $- 64 \sqrt { 3 } + 64 i$ 
D)  $64 \mathrm { i }$

Question 2

Is the given number z in the Julia set?
-z = -0.6i

Accepted Answer

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

Question 3

Use the parallelogram rule to find the magnitude of the resultant force for the two forces shown in the figure. Round to
one decimal place.
-A force of $24 \mathrm { lb }$ is required to hold a $61 \mathrm { lb }$ toolbox on an incline. What angle does the incline make with the horizontal?

Accepted Answer

A)  $23.2 ^ { \circ }$ 
B)  $66.8 ^ { \circ }$ 
C)  $78.7 ^ { \circ }$ 
D)  $11.3 ^ { \circ }$ 
A)  $23.2 ^ { \circ }$ 
B)  $66.8 ^ { \circ }$ 
C)  $78.7 ^ { \circ }$ 
D)  $11.3 ^ { \circ }$

Question 4

Solve the problem.
-If u =-5, 3 , v =6, -6 , and w =-3, 12, evaluate u ·w + v ·w.

Accepted Answer

A)  -39 
B)  -34 
C)  -32 
D)  -43 
A)  -39 
B)  -34 
C)  -32 
D)  -43

Question 5

The rectangular coordinates of a point are given. Express the point in polar coordinates with $$r \geq 0 \text { and } 0 ^ { \circ } \leq \theta < 360 ^ { \circ } \text {. }$$
-$\left[ 0 , \frac { 1 } { 5 } \right)$

Accepted Answer

A)  $\left( \frac { 1 } { 5 } , 0 ^ { \circ } \right)$ 
B)  $\left( \frac { 1 } { 5 } , 360 ^ { \circ } \right)$ 
C)  $\left( \frac { 1 } { 5 } , 90 ^ { \circ } \right)$ 
D)  $\left( - \frac { 1 } { 5 } , 0 ^ { \circ } \right)$ 
A)  $\left( \frac { 1 } { 5 } , 0 ^ { \circ } \right)$ 
B)  $\left( \frac { 1 } { 5 } , 360 ^ { \circ } \right)$ 
C)  $\left( \frac { 1 } { 5 } , 90 ^ { \circ } \right)$ 
D)  $\left( - \frac { 1 } { 5 } , 0 ^ { \circ } \right)$

Question 6

Graph the cycloid for t in the indicated interval.
-$$x = 5 ( t - \sin t ) , y = 5 ( 1 - \cos t ) , 0 \leq t \leq 4 \pi$$

Accepted Answer

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

Question 7

Find the dot product for the pair of vectors.
-i + 4j, 7i - j

Accepted Answer

A)  0 
B)  -3 
C)  3 
D)  11 
A)  0 
B)  -3 
C)  3 
D)  11

Question 8

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form.
-$$\frac { 5 \left( \cos 200 ^ { \circ } + i \sin 200 ^ { \circ } \right) } { 4 \left( \cos 50 ^ { \circ } + i \sin 50 ^ { \circ } \right) }$$

Accepted Answer

A)  $- 10 + 10 \sqrt { 3 } i$ 
B)  $- \frac { 5 \sqrt { 3 } } { 8 } + \frac { 5 } { 8 } i$ 
C)  $- 2 + 2 \sqrt { 3 } i$ 
D)  $- \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } \mathrm { i }$ 
A)  $- 10 + 10 \sqrt { 3 } i$ 
B)  $- \frac { 5 \sqrt { 3 } } { 8 } + \frac { 5 } { 8 } i$ 
C)  $- 2 + 2 \sqrt { 3 } i$ 
D)  $- \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } \mathrm { i }$

Question 9

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.
-A room in the shape of a triangle has sides of length $17.8$ yards, $14.1$ yards, and $13.4$ yards. If carpeting costs $\$ 20.83$ per square yard, padding costs $\$ 1.60$ per square yard, and there is no charge for installation, how much, to the nearest dollar, will it cost to carpet the room?

Accepted Answer

A)  $\$ 93$ 
B)  $\$ 3363$ 
C)  $\$ 439$ 
D)  $\$ 2091$ 
A)  $\$ 93$ 
B)  $\$ 3363$ 
C)  $\$ 439$ 
D)  $\$ 2091$

Question 10

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form.
-$$\frac { \sqrt { 3 } \left( \cos \frac { 7 \pi } { 4 } + i \sin \frac { 7 \pi } { 4 } \right) } { \sqrt { 6 } \left( \cos \frac { 9 \pi } { 4 } + i \sin \frac { 9 \pi } { 4 } \right) }$$

Accepted Answer

A)  $- \frac { \sqrt { 2 } } { 2 } - \frac { \sqrt { 2 } } { 2 } i$ 
B)  $\frac { \sqrt { 2 } } { 2 } + \frac { \sqrt { 2 } } { 2 }$ i 
C)  $\frac { \sqrt { 2 } } { 2 }$ 
D)  $- \frac { \sqrt { 2 } } { 2 } i$ 
A)  $- \frac { \sqrt { 2 } } { 2 } - \frac { \sqrt { 2 } } { 2 } i$ 
B)  $\frac { \sqrt { 2 } } { 2 } + \frac { \sqrt { 2 } } { 2 }$ i 
C)  $\frac { \sqrt { 2 } } { 2 }$ 
D)  $- \frac { \sqrt { 2 } } { 2 } i$

Question 11

Sketch the vectors u and w with angle $\theta$ between them and sketch the resultant.
-$$| \mathbf { u } | = 5 , | \mathbf { w } | = 1 , \theta = 60 ^ { \circ }$$

Accepted Answer

A) 
  
B) 
  
A) 
  
B)

Question 12

Use a table of values to graph the plane curve defined by the following parametric equations. Find a rectangular equation
for the curve.
-$$x = 2 t - 1 , y = t ^ { 2 } + 6 \text {, for } t \text { in } [ - 4,4 ]$$

Accepted Answer

A) 
 
$y = x ^ { 2 } + 1$, for $x$ in $[ - 2,2 ]$ 
B) 
 
 $y = \frac { 1 } { 4 } x ^ { 2 } + \frac { 1 } { 2 } x + \frac { 25 } { 4 }$, for $x$ in $[ - 9,7 ]$ 
C) 
 
$$y = \frac { 1 } { 2 } x ^ { 2 } + 1 , \text { for } x \text { in } [ - 6,4 ]$$ 
D) 
 
$$y = - \frac { 1 } { 2 } x + 30 \text {, for } x \text { in } [ - 6,4 ]$$ 
A) 
 
$y = x ^ { 2 } + 1$, for $x$ in $[ - 2,2 ]$ 
B) 
 
 $y = \frac { 1 } { 4 } x ^ { 2 } + \frac { 1 } { 2 } x + \frac { 25 } { 4 }$, for $x$ in $[ - 9,7 ]$ 
C) 
 
$$y = \frac { 1 } { 2 } x ^ { 2 } + 1 , \text { for } x \text { in } [ - 6,4 ]$$ 
D) 
 
$$y = - \frac { 1 } { 2 } x + 30 \text {, for } x \text { in } [ - 6,4 ]$$

Question 13

Find the indicated vector.
-Let $\mathbf { u } = \langle - 2 , - 6 \rangle$. Find $5 \mathbf { u }$.

Accepted Answer

A)  $\langle 10 , - 30 \rangle$ 
B)  $\langle - 10 , - 30 \rangle$ 
C)  $\langle - 10,30 \rangle$ 
D)  $\langle 10,30 \rangle$ 
A)  $\langle 10 , - 30 \rangle$ 
B)  $\langle - 10 , - 30 \rangle$ 
C)  $\langle - 10,30 \rangle$ 
D)  $\langle 10,30 \rangle$

Question 14

Find the indicated angle or side. Give an exact answer.
-Find the measure of angle A in degrees.

Accepted Answer

A)  $120 ^ { \circ }$ 
B)  $30 ^ { \circ }$ 
C)  $45 ^ { \circ }$ 
D)  $60 ^ { \circ }$ 
A)  $120 ^ { \circ }$ 
B)  $30 ^ { \circ }$ 
C)  $45 ^ { \circ }$ 
D)  $60 ^ { \circ }$

Question 15

Solve the problem.
-To find the distance $\mathrm { AB }$ across a river, a distance $\mathrm { BC } = 1101 \mathrm {~m}$ is laid off on one side of the river. It is found that $\mathrm { B } = 112.8 ^ { \circ }$ and $\mathrm { C } = 12.0 ^ { \circ }$. Find $\mathrm { AB }$ rounded to the nearest meter.

Accepted Answer

A)  $230 \mathrm {~m}$ 
B)  $279 \mathrm {~m}$ 
C)  $282 \mathrm {~m}$ 
D)  $233 \mathrm {~m}$ 
A)  $230 \mathrm {~m}$ 
B)  $279 \mathrm {~m}$ 
C)  $282 \mathrm {~m}$ 
D)  $233 \mathrm {~m}$

Question 16

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

Accepted Answer

A) 
  
B) 
  
A) 
  
B)

Question 17

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form.
-$$\frac { - 2 } { 5 - 4 \mathrm { i } }$$

Accepted Answer

A)  $- \frac { 10 } { 9 } - \frac { 8 } { 9 } \mathrm { i }$ 
B)  $- \frac { 10 } { 41 } + \frac { 8 } { 41 } \mathrm { i }$ 
C)  $- \frac { 10 } { 9 } + \frac { 8 } { 9 } \mathrm { i }$ 
D)  $- \frac { 10 } { 41 } - \frac { 8 } { 41 } \mathrm { i }$ 
A)  $- \frac { 10 } { 9 } - \frac { 8 } { 9 } \mathrm { i }$ 
B)  $- \frac { 10 } { 41 } + \frac { 8 } { 41 } \mathrm { i }$ 
C)  $- \frac { 10 } { 9 } + \frac { 8 } { 9 } \mathrm { i }$ 
D)  $- \frac { 10 } { 41 } - \frac { 8 } { 41 } \mathrm { i }$

Question 18

Use the parallelogram rule to find the magnitude of the resultant force for the two forces shown in the figure. Round to
one decimal place.
-What is the minimum force required to prevent a ball weighing $20.7 \mathrm { lb }$ from rolling down a ramp inclined $12.2 ^ { \circ }$ with the horizontal?

Accepted Answer

A)  $4.4 \mathrm { lb }$ 
B)  $10.1 \mathrm { lb }$ 
C)  $2.2 \mathrm { lb }$ 
D)  $20.2 \mathrm { lb }$ 
A)  $4.4 \mathrm { lb }$ 
B)  $10.1 \mathrm { lb }$ 
C)  $2.2 \mathrm { lb }$ 
D)  $20.2 \mathrm { lb }$

Question 19

Draw a sketch to represent the vector. Refer to the vectors pictured here.  
-3d

Accepted Answer

A) 
  
B) 
  
A) 
  
B)

Question 20

Find the product. Write the product in rectangular form, using exact values.
-$\left[ 8 \left( \cos 210 ^ { \circ } + i \sin 210 ^ { \circ } \right) \right] \left[ 6 \left( \cos 330 ^ { \circ } + i \sin 330 ^ { \circ } \right) \right]$

Accepted Answer

A)  $12 \sqrt { 3 } + 12 \mathrm { i }$ 
B)  $- 12 + 12 \sqrt { 3 } \mathrm { i }$ 
C)  $24 \mathrm { i }$ 
D)  $- 48$ 
A)  $12 \sqrt { 3 } + 12 \mathrm { i }$ 
B)  $- 12 + 12 \sqrt { 3 } \mathrm { i }$ 
C)  $24 \mathrm { i }$ 
D)  $- 48$

Find the given power. Write answer in rectangular form. - $( - \sqrt { 3 } + i ) ^ { 6 }$

Is the given number z in the Julia set? -z = -0.6i

Use the parallelogram rule to find the magnitude of the resultant force for the two forces shown in the figure. Round to one decimal place. -A force of $24 \mathrm { lb }$ is required to hold a $61 \mathrm { lb }$ toolbox on an incline. What angle does the incline make with the horizontal?

Solve the problem. -If u =-5, 3 , v =6, -6 , and w =-3, 12, evaluate u ·w + v ·w.

The rectangular coordinates of a point are given. Express the point in polar coordinates with $r \geq 0 \text { and } 0 ^ { \circ } \leq \theta < 360 ^ { \circ } \text {. }$ - $\left[ 0 , \frac { 1 } { 5 } \right)$

Graph the cycloid for t in the indicated interval. - $x = 5 ( t - \sin t ) , y = 5 ( 1 - \cos t ) , 0 \leq t \leq 4 \pi$ $Graph the cycloid for t in the indicated interval. - x = 5 ( t - \sin t ) , y = 5 ( 1 - \cos t ) , 0 \leq t \leq 4 \pi$

Find the dot product for the pair of vectors. -i + 4j, 7i - j

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - $\frac { 5 \left( \cos 200 ^ { \circ } + i \sin 200 ^ { \circ } \right) } { 4 \left( \cos 50 ^ { \circ } + i \sin 50 ^ { \circ } \right) }$

Sketch the vectors u and w with angle $\theta$ between them and sketch the resultant. - $| \mathbf { u } | = 5 , | \mathbf { w } | = 1 , \theta = 60 ^ { \circ }$

Find the indicated vector. -Let $\mathbf { u } = \langle - 2 , - 6 \rangle$ . Find $5 \mathbf { u }$ .

Find the indicated angle or side. Give an exact answer. -Find the measure of angle A in degrees.

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

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - $\frac { - 2 } { 5 - 4 \mathrm { i } }$

Use the parallelogram rule to find the magnitude of the resultant force for the two forces shown in the figure. Round to one decimal place. -What is the minimum force required to prevent a ball weighing $20.7 \mathrm { lb }$ from rolling down a ramp inclined $12.2 ^ { \circ }$ with the horizontal?

Draw a sketch to represent the vector. Refer to the vectors pictured here. -3d

Find the product. Write the product in rectangular form, using exact values. - $\left[ 8 \left( \cos 210 ^ { \circ } + i \sin 210 ^ { \circ } \right) \right] \left[ 6 \left( \cos 330 ^ { \circ } + i \sin 330 ^ { \circ } \right) \right]$

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

Find the given power. Write answer in rectangular form. - (−3+i)6( - \sqrt { 3 } + i ) ^ { 6 }(−3​+i)6

Is the given number z in the Julia set? -z = -0.6i

Solve the problem. -If u =-5, 3 , v =6, -6 , and w =-3, 12, evaluate u ·w + v ·w.

The rectangular coordinates of a point are given. Express the point in polar coordinates with r≥0 and 0∘≤θ<360∘. r \geq 0 \text { and } 0 ^ { \circ } \leq \theta < 360 ^ { \circ } \text {. }r≥0 and 0∘≤θ<360∘. - [0,15)\left[ 0 , \frac { 1 } { 5 } \right)[0,51​)

Graph the cycloid for t in the indicated interval. - x=5(t−sin⁡t),y=5(1−cos⁡t),0≤t≤4πx = 5 ( t - \sin t ) , y = 5 ( 1 - \cos t ) , 0 \leq t \leq 4 \pix=5(t−sint),y=5(1−cost),0≤t≤4π

Find the dot product for the pair of vectors. -i + 4j, 7i - j

Sketch the vectors u and w with angle θ\thetaθ between them and sketch the resultant. - ∣u∣=5,∣w∣=1,θ=60∘| \mathbf { u } | = 5 , | \mathbf { w } | = 1 , \theta = 60 ^ { \circ }∣u∣=5,∣w∣=1,θ=60∘

Use a table of values to graph the plane curve defined by the following parametric equations. Find a rectangular equation for the curve. - x=2t−1,y=t2+6, for t in [−4,4]x = 2 t - 1 , y = t ^ { 2 } + 6 \text {, for } t \text { in } [ - 4,4 ]x=2t−1,y=t2+6, for t in [−4,4]

Find the indicated vector. -Let u=⟨−2,−6⟩\mathbf { u } = \langle - 2 , - 6 \rangleu=⟨−2,−6⟩ . Find 5u5 \mathbf { u }5u .

Find the indicated angle or side. Give an exact answer. -Find the measure of angle A in degrees.

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

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - −25−4i\frac { - 2 } { 5 - 4 \mathrm { i } }5−4i−2​

Draw a sketch to represent the vector. Refer to the vectors pictured here. -3d

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

Find the given power. Write answer in rectangular form. - $( - \sqrt { 3 } + i ) ^ { 6 }$

The rectangular coordinates of a point are given. Express the point in polar coordinates with $r \geq 0 \text { and } 0 ^ { \circ } \leq \theta < 360 ^ { \circ } \text {. }$ - $\left[ 0 , \frac { 1 } { 5 } \right)$

Graph the cycloid for t in the indicated interval. - $x = 5 ( t - \sin t ) , y = 5 ( 1 - \cos t ) , 0 \leq t \leq 4 \pi$ $Graph the cycloid for t in the indicated interval. - x = 5 ( t - \sin t ) , y = 5 ( 1 - \cos t ) , 0 \leq t \leq 4 \pi$

Sketch the vectors u and w with angle $\theta$ between them and sketch the resultant. - $| \mathbf { u } | = 5 , | \mathbf { w } | = 1 , \theta = 60 ^ { \circ }$

Find the indicated vector. -Let $\mathbf { u } = \langle - 2 , - 6 \rangle$ . Find $5 \mathbf { u }$ .

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - $\frac { - 2 } { 5 - 4 \mathrm { i } }$