Question 1

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

Accepted Answer

A)   
B)   
A)   
B)

Question 2

Find the component form of the indicated vector.
-Let $\mathbf { u } = \langle 6,3 \rangle$. Find $- 2 \mathbf { u }$.

Accepted Answer

A)  $\langle 12,6 \rangle$ 
B)  $\langle 12 , - 6 \rangle$ 
C)  $\langle - 12,6 \rangle$ 
D)  $\langle - 12 , - 6 \rangle$ 
A)  $\langle 12,6 \rangle$ 
B)  $\langle 12 , - 6 \rangle$ 
C)  $\langle - 12,6 \rangle$ 
D)  $\langle - 12 , - 6 \rangle$

Question 3

Find the indicated vector.
-Let $\mathbf { a } = \langle 1 , - 8 \rangle$. Find $- 4 \mathbf { a }$.

Accepted Answer

A)  $\langle 4,32 \rangle$ 
B)  $\langle 4 , - 32 \rangle$ 
C)  $\langle - 4 , - 32 \rangle$ 
D)  $\langle - 4,32 \rangle$ 
A)  $\langle 4,32 \rangle$ 
B)  $\langle 4 , - 32 \rangle$ 
C)  $\langle - 4 , - 32 \rangle$ 
D)  $\langle - 4,32 \rangle$

Question 4

Solve the problem.
-The current $\mathrm { I }$ in a circuit with voltage $\mathrm { E }$, resistance $\mathrm { R }$, capacitive reactance $X _ { \mathrm { C } }$ and inductive reactance $X _ { L }$ is
$$I = \frac { E } { R + \left( X _ { L } - X _ { C } \right) i }$$
Find $\mathrm { I }$ if $\mathrm { E } = 2 \sqrt { 2 } \left( \cos 45 ^ { \circ } + i \sin 45 ^ { \circ } \right) , \mathrm { R } = 4 , \mathrm { X } _ { \mathrm { L } } = 8$, and $\mathrm { X } _ { \mathrm { C } } = 6$
Give your answer in rectangular form.

Accepted Answer

A)  $\frac { 1 } { 5 } + \frac { 1 } { 5 } \mathrm { i }$ 
B)  $\frac { 1 } { 5 } + \frac { 3 } { 5 } \mathrm { i }$ 
C)  $\frac { 3 } { 5 } + \frac { 3 } { 5 } \mathrm { i }$ 
D)  $\frac { 3 } { 5 } + \frac { 1 } { 5 } \mathrm { i }$ 
A)  $\frac { 1 } { 5 } + \frac { 1 } { 5 } \mathrm { i }$ 
B)  $\frac { 1 } { 5 } + \frac { 3 } { 5 } \mathrm { i }$ 
C)  $\frac { 3 } { 5 } + \frac { 3 } { 5 } \mathrm { i }$ 
D)  $\frac { 3 } { 5 } + \frac { 1 } { 5 } \mathrm { i }$

Question 5

Plot the point.
-$$\left( - 4 , \frac { 7 \pi } { 4 } \right)$$

Accepted Answer

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

Question 6

Solve the problem.
-A projectile is fired with an initial velocity of 450 feet per second at an angle of $45 ^ { \circ }$ with the horizontal. In how many seconds will the projectile strike the ground? (Round your answer to the nearest tenth of a second.)

Accepted Answer

A)  $24.7 \mathrm { sec }$ 
B)  $16.5 \mathrm { sec }$ 
C)  $28 \mathrm { sec }$ 
D)  $19.9 \mathrm { sec }$ 
A)  $24.7 \mathrm { sec }$ 
B)  $16.5 \mathrm { sec }$ 
C)  $28 \mathrm { sec }$ 
D)  $19.9 \mathrm { sec }$

Question 7

Solve the problem.
-If $\mathbf { u } = \langle - 5,7 \rangle , \mathbf { v } = \langle - 7,6 \rangle$, and $\mathbf { w } = \langle - 11,2 \rangle$, evaluate $\mathbf { u } \cdot ( \mathbf { v } - \mathbf { w } )$.

Accepted Answer

A)  35 
B)  12 
C)  3 
D)  8 
A)  35 
B)  12 
C)  3 
D)  8

Question 8

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

Accepted Answer

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

Question 9

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.
-$$\begin{array} { l } 
\mathrm { A } = 41 ^ { \circ } 20 ^ { \prime } \
\mathrm { b } = 17.6 \mathrm {~m} \
\mathrm { c } = 9.2 \mathrm {~m}
\end{array}$$

Accepted Answer

A)  $53.5 \mathrm {~m} ^ { 2 }$ 
B)  $26.8 \mathrm {~m} ^ { 2 }$ 
C)  $109 \mathrm {~m} ^ { 2 }$ 
D)  $107 \mathrm {~m} ^ { 2 }$ 
A)  $53.5 \mathrm {~m} ^ { 2 }$ 
B)  $26.8 \mathrm {~m} ^ { 2 }$ 
C)  $109 \mathrm {~m} ^ { 2 }$ 
D)  $107 \mathrm {~m} ^ { 2 }$

Question 10

The rectangular coordinates of a point are given. Express the point in polar coordinates with r ≥ 0 and 0° ≤ θ < 360°.
-$\left( 0 , \frac { 1 } { 4 } \right)$

Accepted Answer

A)  $\left( - \frac { 1 } { 4 } , 0 ^ { \circ } \right)$ 
B)  $\left( \frac { 1 } { 4 } , 90 ^ { \circ } \right)$ 
C)  $\left( \frac { 1 } { 4 } , 360 ^ { \circ } \right)$ 
D)  $\left( \frac { 1 } { 4 } , 0 ^ { \circ } \right)$ 
A)  $\left( - \frac { 1 } { 4 } , 0 ^ { \circ } \right)$ 
B)  $\left( \frac { 1 } { 4 } , 90 ^ { \circ } \right)$ 
C)  $\left( \frac { 1 } { 4 } , 360 ^ { \circ } \right)$ 
D)  $\left( \frac { 1 } { 4 } , 0 ^ { \circ } \right)$

Question 11

Find a rectangular equation for the plane curve defined by the parametric equations.
-$x = \sec t , y = \tan t$

Accepted Answer

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

Question 12

Graph the complex number.
-$$- 4 + i$$

Accepted Answer

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

Question 13

Solve the problem.
-Suppose that a radio transmission pattern can be modeled by $\mathrm { r } ^ { 2 } = 10,000 \sin 2 \theta$, for $0 ^ { \circ } \leq \theta \leq 360 ^ { \circ }$, where the units are miles. Determine the predominant direction(s) of transmission and the distance(s) of transmission in such direction(s). Assume that the positive $x$-axis points east.

Accepted Answer

A)  Northeast; 100 miles 
B)  Northeast and southwest; 100 miles 
C)  North and south; 100 miles 
D)  Northeast and southwest; 10,000 miles 
A)  Northeast; 100 miles 
B)  Northeast and southwest; 100 miles 
C)  North and south; 100 miles 
D)  Northeast and southwest; 10,000 miles

Question 14

Solve the problem.
-A painter needs to cover a triangular region 65 meters by 67 meters by 75 meters. A can of paint covers 70 square meters. How many cans will be needed?

Accepted Answer

A)  3 cans 
B)  15 cans 
C)  333 cans 
D)  30 cans 
A)  3 cans 
B)  15 cans 
C)  333 cans 
D)  30 cans

Question 15

Write the word or phrase that best completes each statement or answers the question.
-Which of the following pairs of parametric equations will graph a semicircle?

Accepted Answer

A)  $x = \cos 2 t , y = \sin 2 t , 0 \leq t \leq \pi$ 
B)  $x = \cos t , y = \sin t , 0 \leq t \leq \frac { \pi } { 2 }$ 
C)  $x = \cos \frac { 1 } { 4 } t , y = \sin \frac { 1 } { 4 } t , 0 \leq t \leq 4 \pi$ 
D)  $x = \cos \frac { 1 } { 2 } \mathrm { t } , \mathrm { y } = \sin \frac { 1 } { 2 } \mathrm { t } , 0 \leq \mathrm { t } \leq \pi$ 
A)  $x = \cos 2 t , y = \sin 2 t , 0 \leq t \leq \pi$ 
B)  $x = \cos t , y = \sin t , 0 \leq t \leq \frac { \pi } { 2 }$ 
C)  $x = \cos \frac { 1 } { 4 } t , y = \sin \frac { 1 } { 4 } t , 0 \leq t \leq 4 \pi$ 
D)  $x = \cos \frac { 1 } { 2 } \mathrm { t } , \mathrm { y } = \sin \frac { 1 } { 2 } \mathrm { t } , 0 \leq \mathrm { t } \leq \pi$

Question 16

Find all cube roots of the complex number. Leave answers in trigonometric form.
-$64 \mathrm { i }$

Accepted Answer

A)  $1 , - 1 , - i$ 
B)  $4 \operatorname { cis } 0 ^ { \circ } , 4 \operatorname { cis } 120 ^ { \circ } , 4 \operatorname { cis } 240 ^ { \circ }$ 
C)  $4 \operatorname { cis } 30 ^ { \circ } , 4 \operatorname { cis } 150 ^ { \circ } , 4 \operatorname { cis } 270 ^ { \circ }$ 
D)  $4 \operatorname { cis } 60 ^ { \circ } , 4 \operatorname { cis } 180 ^ { \circ } , 4 \operatorname { cis } 300 ^ { \circ }$ 
A)  $1 , - 1 , - i$ 
B)  $4 \operatorname { cis } 0 ^ { \circ } , 4 \operatorname { cis } 120 ^ { \circ } , 4 \operatorname { cis } 240 ^ { \circ }$ 
C)  $4 \operatorname { cis } 30 ^ { \circ } , 4 \operatorname { cis } 150 ^ { \circ } , 4 \operatorname { cis } 270 ^ { \circ }$ 
D)  $4 \operatorname { cis } 60 ^ { \circ } , 4 \operatorname { cis } 180 ^ { \circ } , 4 \operatorname { cis } 300 ^ { \circ }$

Question 17

Determine two pairs of polar coordinates for the point with 0° ≤ θ < 360°.
-$( 5 \sqrt { 3 } , 15 )$

Accepted Answer

A)  $\left( 10 \sqrt { 3 } , 300 ^ { \circ } \right) , \left( - 10 \sqrt { 3 } , 60 ^ { \circ } \right)$ 
B)  $\left( 10 \sqrt { 3 } , 30 ^ { \circ } \right) , \left( - 15 \sqrt { 3 } , 330 ^ { \circ } \right)$ 
C)  $\left( 10 \sqrt { 3 } , 30 ^ { \circ } \right) , \left( - 10 \sqrt { 3 } , 330 ^ { \circ } \right)$ 
D)  $\left( 10 \sqrt { 3 } , 60 ^ { \circ } \right) , \left( - 10 \sqrt { 3 } , 240 ^ { \circ } \right)$ 
A)  $\left( 10 \sqrt { 3 } , 300 ^ { \circ } \right) , \left( - 10 \sqrt { 3 } , 60 ^ { \circ } \right)$ 
B)  $\left( 10 \sqrt { 3 } , 30 ^ { \circ } \right) , \left( - 15 \sqrt { 3 } , 330 ^ { \circ } \right)$ 
C)  $\left( 10 \sqrt { 3 } , 30 ^ { \circ } \right) , \left( - 10 \sqrt { 3 } , 330 ^ { \circ } \right)$ 
D)  $\left( 10 \sqrt { 3 } , 60 ^ { \circ } \right) , \left( - 10 \sqrt { 3 } , 240 ^ { \circ } \right)$

Question 18

Solve the problem.
-If $\mathbf { u } = \langle - 5,7 \rangle , \mathbf { v } = \langle 8,6 \rangle$, and $\mathbf { w } = \langle - 11,2 \rangle$, evaluate $\mathbf { u } \cdot \mathbf { v } - \mathbf { u } \cdot \mathbf { w }$.

Accepted Answer

A)  $- 40$ 
B)  $- 67$ 
C)  $- 63$ 
D)  $- 72$ 
A)  $- 40$ 
B)  $- 67$ 
C)  $- 63$ 
D)  $- 72$

Question 19

Give two parametric representations for the equation of the parabola.
-$$y = x ^ { 2 } + 6 x + 11$$

Accepted Answer

A)  $x = t , y = t ^ { 2 } + 6 t + 11$ for $t$ in $( - \infty , \infty ) ; x = t - 3 , y = t ^ { 2 } + 2$ for $t$ in $( - \infty , \infty )$ 
B)  $x = t , y = t ^ { 2 } - 6 t - 11$ for $t$ in $( - \infty , \infty ) ; x = t + 3 , y = t ^ { 2 } + 2$ for $t$ in $( - \infty , \infty )$ 
C)  $x = t , y = t ^ { 2 } + 6 t + 11$ for $t$ in $( - \infty , \infty ) ; x = t - 3 , y = t ^ { 2 } - 2$ for $t$ in $( - \infty , \infty )$ 
D)  $x = t , y = t ^ { 2 } + 6 t + 11$ for $t$ in $( - \infty , \infty ) ; x = t + 3 , y = t ^ { 2 } + 2$ for $t$ in $( - \infty , \infty )$ 
A)  $x = t , y = t ^ { 2 } + 6 t + 11$ for $t$ in $( - \infty , \infty ) ; x = t - 3 , y = t ^ { 2 } + 2$ for $t$ in $( - \infty , \infty )$ 
B)  $x = t , y = t ^ { 2 } - 6 t - 11$ for $t$ in $( - \infty , \infty ) ; x = t + 3 , y = t ^ { 2 } + 2$ for $t$ in $( - \infty , \infty )$ 
C)  $x = t , y = t ^ { 2 } + 6 t + 11$ for $t$ in $( - \infty , \infty ) ; x = t - 3 , y = t ^ { 2 } - 2$ for $t$ in $( - \infty , \infty )$ 
D)  $x = t , y = t ^ { 2 } + 6 t + 11$ for $t$ in $( - \infty , \infty ) ; x = t + 3 , y = t ^ { 2 } + 2$ for $t$ in $( - \infty , \infty )$

Question 20

Solve the problem.
-A projectile is fired with an initial velocity of 450 feet per second at an angle of $$70 ^ { \circ }$$ with the horizontal. In how many seconds will the projectile strike the ground? (Round your answer to the
Nearest tenth of a second.)

Accepted Answer

A)  26.4 sec 
B)  30.5 sec 
C)  23 sec 
D)  29.2 sec 
A)  26.4 sec 
B)  30.5 sec 
C)  23 sec 
D)  29.2 sec

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

Find the component form of the indicated vector. -Let $\mathbf { u } = \langle 6,3 \rangle$ . Find $- 2 \mathbf { u }$ .

Find the indicated vector. -Let $\mathbf { a } = \langle 1 , - 8 \rangle$ . Find $- 4 \mathbf { a }$ .

Plot the point. - $\left( - 4 , \frac { 7 \pi } { 4 } \right)$ $Plot the point. - \left( - 4 , \frac { 7 \pi } { 4 } \right)$

Solve the problem. -A projectile is fired with an initial velocity of 450 feet per second at an angle of $45 ^ { \circ }$ with the horizontal. In how many seconds will the projectile strike the ground? (Round your answer to the nearest tenth of a second.)

Solve the problem. -If $\mathbf { u } = \langle - 5,7 \rangle , \mathbf { v } = \langle - 7,6 \rangle$ , and $\mathbf { w } = \langle - 11,2 \rangle$ , evaluate $\mathbf { u } \cdot ( \mathbf { v } - \mathbf { w } )$ .

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

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary. - =42 =17.6 =9.2

The rectangular coordinates of a point are given. Express the point in polar coordinates with r ≥ 0 and 0° ≤ θ < 360°. - $\left( 0 , \frac { 1 } { 4 } \right)$

Find a rectangular equation for the plane curve defined by the parametric equations. - $x = \sec t , y = \tan t$

Graph the complex number. - $- 4 + i$

Solve the problem. -A painter needs to cover a triangular region 65 meters by 67 meters by 75 meters. A can of paint covers 70 square meters. How many cans will be needed?

Write the word or phrase that best completes each statement or answers the question. -Which of the following pairs of parametric equations will graph a semicircle?

Find all cube roots of the complex number. Leave answers in trigonometric form. - $64 \mathrm { i }$

Determine two pairs of polar coordinates for the point with 0° ≤ θ < 360°. - $( 5 \sqrt { 3 } , 15 )$

Solve the problem. -If $\mathbf { u } = \langle - 5,7 \rangle , \mathbf { v } = \langle 8,6 \rangle$ , and $\mathbf { w } = \langle - 11,2 \rangle$ , evaluate $\mathbf { u } \cdot \mathbf { v } - \mathbf { u } \cdot \mathbf { w }$ .

Give two parametric representations for the equation of the parabola. - $y = x ^ { 2 } + 6 x + 11$

Solve the problem. -A projectile is fired with an initial velocity of 450 feet per second at an angle of $70 ^ { \circ }$ with the horizontal. In how many seconds will the projectile strike the ground? (Round your answer to the Nearest tenth of a second.)

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

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

Find the component form of the indicated vector. -Let u=⟨6,3⟩\mathbf { u } = \langle 6,3 \rangleu=⟨6,3⟩ . Find −2u- 2 \mathbf { u }−2u .

Find the indicated vector. -Let a=⟨1,−8⟩\mathbf { a } = \langle 1 , - 8 \ranglea=⟨1,−8⟩ . Find −4a- 4 \mathbf { a }−4a .

Plot the point. - (−4,7π4)\left( - 4 , \frac { 7 \pi } { 4 } \right)(−4,47π​)

Solve the problem. -A projectile is fired with an initial velocity of 450 feet per second at an angle of 45∘45 ^ { \circ }45∘ with the horizontal. In how many seconds will the projectile strike the ground? (Round your answer to the nearest tenth of a second.)