Question 1

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

Accepted Answer

A)  $\langle 1.71,4.7 \rangle$ 
B)  $\langle 0.94,0.34 \rangle$ 
C)  $\langle 4.7,1.82 \rangle$ 
D)  $\langle 4.7,1.71 \rangle$ 
A)  $\langle 1.71,4.7 \rangle$ 
B)  $\langle 0.94,0.34 \rangle$ 
C)  $\langle 4.7,1.82 \rangle$ 
D)  $\langle 4.7,1.71 \rangle$

Question 2

Graph the cycloid for t in the indicated interval.
-$$x = 7 t - 7 \sin t , y = 7 - 7 \cos t , - 2 \pi \leq t \leq 2 \pi$$

Accepted Answer

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

Question 3

Write the complex number in trigonometric form $$r ( \cos \theta + i \sin \theta )$$ with θ in the interval [0°, 360°).
-$- 6 - 6 \mathrm { i } \sqrt { 3 }$

Accepted Answer

A)  $12 \left( \cos 290 ^ { \circ } + i \sin 290 ^ { \circ } \right)$ 
B)  $6 \left( \cos 240 ^ { \circ } + i \sin 240 ^ { \circ } \right)$ 
C)  $12 \left( \cos 180 ^ { \circ } + i \sin 180 ^ { \circ } \right)$ 
D)  $12 \left( \cos 240 ^ { \circ } + i \sin 240 ^ { \circ } \right)$ 
A)  $12 \left( \cos 290 ^ { \circ } + i \sin 290 ^ { \circ } \right)$ 
B)  $6 \left( \cos 240 ^ { \circ } + i \sin 240 ^ { \circ } \right)$ 
C)  $12 \left( \cos 180 ^ { \circ } + i \sin 180 ^ { \circ } \right)$ 
D)  $12 \left( \cos 240 ^ { \circ } + i \sin 240 ^ { \circ } \right)$

Question 4

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.
-$$\begin{array} { l } 
\mathrm { A } = 38.1 ^ { \circ } \
\mathrm { b } = 12.0 \mathrm { in } . \
\mathrm { c } = 5.5 \mathrm { in } .
\end{array}$$

Accepted Answer

A)  $18.4$ in. $^ { 2 }$ 
B)  26 in. 2 
C)  28 in. 2 
D)  $20.4$ in. ${ } ^ { 2 }$ 
A)  $18.4$ in. $^ { 2 }$ 
B)  26 in. 2 
C)  28 in. 2 
D)  $20.4$ in. ${ } ^ { 2 }$

Question 5

Find all solutions of the equation. Leave answers in trigonometric form.
-$$x ^ { 4 } + 16 = 0$$

Accepted Answer

A)  $\left\{ 2 \operatorname { cis } 45 ^ { \circ } , 2 \operatorname { cis } 315 ^ { \circ } , 2 \right.$ cis $135 ^ { \circ } , 2$ cis $\left. 225 ^ { \circ } \right\}$ 
B)  $\left\{ \sqrt { 3 } \operatorname { cis } 26.565 ^ { \circ } , \sqrt { 3 } \operatorname { cis } 333.435 ^ { \circ } , \sqrt { 3 } \operatorname { cis } 153.435 ^ { \circ } , \sqrt { 3 } \operatorname { cis } 206.565 ^ { \circ } \right\}$ 
C)  $\left\{ 16 \operatorname { cis } 45 ^ { \circ } , 16 \operatorname { cis } 315 ^ { \circ } , 16 \right.$ cis $135 ^ { \circ } , 16$ cis $\left. 225 ^ { \circ } \right\}$ 
D)  $\left\{ \sqrt { 2 } \operatorname { cis } 45 ^ { \circ } , \sqrt { 2 } \operatorname { cis } 315 ^ { \circ } , \sqrt { 2 } \operatorname { cis } 135 ^ { \circ } , \sqrt { 2 } \operatorname { cis } 225 ^ { \circ } \right\}$ 
A)  $\left\{ 2 \operatorname { cis } 45 ^ { \circ } , 2 \operatorname { cis } 315 ^ { \circ } , 2 \right.$ cis $135 ^ { \circ } , 2$ cis $\left. 225 ^ { \circ } \right\}$ 
B)  $\left\{ \sqrt { 3 } \operatorname { cis } 26.565 ^ { \circ } , \sqrt { 3 } \operatorname { cis } 333.435 ^ { \circ } , \sqrt { 3 } \operatorname { cis } 153.435 ^ { \circ } , \sqrt { 3 } \operatorname { cis } 206.565 ^ { \circ } \right\}$ 
C)  $\left\{ 16 \operatorname { cis } 45 ^ { \circ } , 16 \operatorname { cis } 315 ^ { \circ } , 16 \right.$ cis $135 ^ { \circ } , 16$ cis $\left. 225 ^ { \circ } \right\}$ 
D)  $\left\{ \sqrt { 2 } \operatorname { cis } 45 ^ { \circ } , \sqrt { 2 } \operatorname { cis } 315 ^ { \circ } , \sqrt { 2 } \operatorname { cis } 135 ^ { \circ } , \sqrt { 2 } \operatorname { cis } 225 ^ { \circ } \right\}$

Question 6

Find all specified roots.
-Cube roots of $i$.

Accepted Answer

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

Question 7

Write the complex number in rectangular form.
-$3 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$

Accepted Answer

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

Question 8

Solve the problem.
-A solar reflector is made using 35 identical triangular-shaped mirrors, each having sides 2 meters, 1.7 meters, 1.5 meters. What is the total surface area of the reflector (to the nearest square meter)?

Accepted Answer

A)  $54 \mathrm {~m} ^ { 2 }$ 
B)  $38 \mathrm {~m} ^ { 2 }$ 
C)  $43 \mathrm {~m} ^ { 2 }$ 
D)  $36 \mathrm {~m} ^ { 2 }$ 
A)  $54 \mathrm {~m} ^ { 2 }$ 
B)  $38 \mathrm {~m} ^ { 2 }$ 
C)  $43 \mathrm {~m} ^ { 2 }$ 
D)  $36 \mathrm {~m} ^ { 2 }$

Question 9

The rectangular coordinates of a point are given. Express the point in polar coordinates with r ≥ 0 and 0° ≤ θ < 360°.
-$\left( \frac { 1 } { 3 } , \frac { \sqrt { 3 } } { 3 } \right)$

Accepted Answer

A)  $\left( \frac { 2 } { 3 } , 120 ^ { \circ } \right)$ 
B)  $\left( \frac { 1 } { 3 } , 30 ^ { \circ } \right)$ 
C)  $\left( \frac { 2 } { 3 } , 30 ^ { \circ } \right)$ 
D)  $\left( \frac { 2 } { 3 } , 60 ^ { \circ } \right)$ 
A)  $\left( \frac { 2 } { 3 } , 120 ^ { \circ } \right)$ 
B)  $\left( \frac { 1 } { 3 } , 30 ^ { \circ } \right)$ 
C)  $\left( \frac { 2 } { 3 } , 30 ^ { \circ } \right)$ 
D)  $\left( \frac { 2 } { 3 } , 60 ^ { \circ } \right)$

Question 10

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 smallest possible distance between Earth, for which $\mathrm { a } = 1.00$ and $\mathrm { e } = 0.017$, and Venus, for which $\mathrm { a } = 0.78$ and $\mathrm { e } = 0.007$.

Accepted Answer

A)  Zero astronomical units 
B)  About $0.2$ astronomical units 
C)  About $0.4$ astronomical units 
D)  About 2 astronomical units 
A)  Zero astronomical units 
B)  About $0.2$ astronomical units 
C)  About $0.4$ astronomical units 
D)  About 2 astronomical units

Question 11

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

Accepted Answer

A)  $r = 6 \cos \theta$ 
B)  $r = 6 \sin \theta$ 
C)  $r \sin \theta = 3$ 
D)  $r = 3$ 
A)  $r = 6 \cos \theta$ 
B)  $r = 6 \sin \theta$ 
C)  $r \sin \theta = 3$ 
D)  $r = 3$

Question 12

Find all cube roots of the complex number. Leave answers in trigonometric form.
-$- 3 \sqrt { 3 } + 3 i$

Accepted Answer

A)  $\sqrt [ 3 ] { 3 } \operatorname { cis } 70 ^ { \circ } , \sqrt [ 3 ] { 3 } \operatorname { cis } 190 ^ { \circ } , \sqrt [ 3 ] { 3 } \operatorname { cis } 310 ^ { \circ }$ 
B)  $\sqrt { 3 } \operatorname { cis } 70 ^ { \circ } , \sqrt { 3 } \operatorname { cis } 190 ^ { \circ } , \sqrt { 3 } \operatorname { cis } 310 ^ { \circ }$ 
C)  $\sqrt [ 3 ] { 6 } \operatorname { cis } 50 ^ { \circ } , \sqrt [ 3 ] { 6 } \operatorname { cis } 170 ^ { \circ } , \sqrt [ 3 ] { 6 } \operatorname { cis } 290 ^ { \circ }$ 
D)  $\sqrt [ 3 ] { 6 } \operatorname { cis } 50 ^ { \circ } , \sqrt [ 3 ] { 6 } \operatorname { cis } 170 ^ { \circ } , \sqrt [ 3 ] { 6 } \operatorname { cis } 270 ^ { \circ }$ 
A)  $\sqrt [ 3 ] { 3 } \operatorname { cis } 70 ^ { \circ } , \sqrt [ 3 ] { 3 } \operatorname { cis } 190 ^ { \circ } , \sqrt [ 3 ] { 3 } \operatorname { cis } 310 ^ { \circ }$ 
B)  $\sqrt { 3 } \operatorname { cis } 70 ^ { \circ } , \sqrt { 3 } \operatorname { cis } 190 ^ { \circ } , \sqrt { 3 } \operatorname { cis } 310 ^ { \circ }$ 
C)  $\sqrt [ 3 ] { 6 } \operatorname { cis } 50 ^ { \circ } , \sqrt [ 3 ] { 6 } \operatorname { cis } 170 ^ { \circ } , \sqrt [ 3 ] { 6 } \operatorname { cis } 290 ^ { \circ }$ 
D)  $\sqrt [ 3 ] { 6 } \operatorname { cis } 50 ^ { \circ } , \sqrt [ 3 ] { 6 } \operatorname { cis } 170 ^ { \circ } , \sqrt [ 3 ] { 6 } \operatorname { cis } 270 ^ { \circ }$

Question 13

Answer the question.
-On which line do the square roots of $- \mathrm { i }$ lie?

Accepted Answer

A)  The line $y = 1$ 
B)  The line $y = x$ 
C)  The line $y = - x$ 
D)  The line $y = 0$. 
A)  The line $y = 1$ 
B)  The line $y = x$ 
C)  The line $y = - x$ 
D)  The line $y = 0$.

Question 14

Find the missing parts of the triangle.
-$$\begin{array} { l } 
\mathrm { C } = 35 ^ { \circ } 30 ^ { \prime } \
\mathrm { a } = 18.76 \
\mathrm { c } = 16.15
\end{array}$$
If necessary, round side lengths to the nearest hundredth.

Accepted Answer

A)  $\mathrm { A } = 42 ^ { \circ } 25 ^ { \prime } , \mathrm { B } = 102 ^ { \circ } 05 ^ { \prime } , \mathrm { b } = 25.19$ 
B)  $\mathrm { A } _ { 1 } = 42 ^ { \circ } 25 ^ { \prime } , \mathrm { B } _ { 1 } = 102 ^ { \circ } 05 ^ { \prime } , \mathrm { b } _ { 1 } = 27.2$;
$$\mathrm { A } _ { 2 } = 137 ^ { \circ } 35 ^ { \prime } , \mathrm { B } _ { 2 } = 6 ^ { \circ } 55 ^ { \prime } , \mathrm { b } _ { 2 } = 3.35$$ 
C)  no such triangle 
D)  $\mathrm { A } _ { 1 } = 102 ^ { \circ } 05 ^ { \prime } , \mathrm { B } _ { 1 } = 42 ^ { \circ } 25 ^ { \prime } , \mathrm { b } _ { 1 } = 17.52$;
$\mathrm { A } _ { 2 } = 6 ^ { \circ } 55 ^ { \prime } , \mathrm { B } _ { 2 } = 137 ^ { \circ } 35 ^ { \prime } , \mathrm { b } _ { 2 } = 26.19$ 
A)  $\mathrm { A } = 42 ^ { \circ } 25 ^ { \prime } , \mathrm { B } = 102 ^ { \circ } 05 ^ { \prime } , \mathrm { b } = 25.19$ 
B)  $\mathrm { A } _ { 1 } = 42 ^ { \circ } 25 ^ { \prime } , \mathrm { B } _ { 1 } = 102 ^ { \circ } 05 ^ { \prime } , \mathrm { b } _ { 1 } = 27.2$;
$$\mathrm { A } _ { 2 } = 137 ^ { \circ } 35 ^ { \prime } , \mathrm { B } _ { 2 } = 6 ^ { \circ } 55 ^ { \prime } , \mathrm { b } _ { 2 } = 3.35$$ 
C)  no such triangle 
D)  $\mathrm { A } _ { 1 } = 102 ^ { \circ } 05 ^ { \prime } , \mathrm { B } _ { 1 } = 42 ^ { \circ } 25 ^ { \prime } , \mathrm { b } _ { 1 } = 17.52$;
$\mathrm { A } _ { 2 } = 6 ^ { \circ } 55 ^ { \prime } , \mathrm { B } _ { 2 } = 137 ^ { \circ } 35 ^ { \prime } , \mathrm { b } _ { 2 } = 26.19$

Question 15

Give the rectangular coordinates for the point.
-$( 5 , \pi )$

Accepted Answer

A)  $( 0,5 )$ 
B)  $( 5,0 )$ 
C)  $( 0 , - 5 )$ 
D)  $( - 5,0 )$ 
A)  $( 0,5 )$ 
B)  $( 5,0 )$ 
C)  $( 0 , - 5 )$ 
D)  $( - 5,0 )$

Question 16

Solve the problem.
-A force of $670 \mathrm { lb }$ is required to pull a boat up a ramp inclined at $25 ^ { \circ }$ with the horizontal. How much does the boat weigh?

Accepted Answer

A)  $645 \mathrm { lb }$ 
B)  $1585 \mathrm { lb }$ 
C)  $607 \mathrm { lb }$ 
D)  $2192 \mathrm { lb }$ 
A)  $645 \mathrm { lb }$ 
B)  $1585 \mathrm { lb }$ 
C)  $607 \mathrm { lb }$ 
D)  $2192 \mathrm { lb }$

Question 17

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

Accepted Answer

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

Question 18

Give the rectangular coordinates for the point.
-$\left( 2,90 ^ { \circ } \right)$

Accepted Answer

A)  $( - 2,0 )$ 
B)  $( 0,2 )$ 
C)  $( 2,0 )$ 
D)  $( 0 , - 2 )$ 
A)  $( - 2,0 )$ 
B)  $( 0,2 )$ 
C)  $( 2,0 )$ 
D)  $( 0 , - 2 )$

Question 19

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations.
-$$x = t ^ { 2 } - 9 , y = t ^ { 2 } + 8 ; t = 3$$

Accepted Answer

A)  $( 18,1 )$ 
B)  $( 1,18 )$ 
C)  $( 17,0 )$ 
D)  $( 0,17 )$ 
A)  $( 18,1 )$ 
B)  $( 1,18 )$ 
C)  $( 17,0 )$ 
D)  $( 0,17 )$

Question 20

Solve the problem.
-If $\mathbf { u } = \langle - 3,5 \rangle$ and $\mathbf { v } = \langle 4,9 \rangle$, evaluate $( 2 \mathbf { u } ) \cdot \mathbf { v }$.

Accepted Answer

A)  102 
B)  72 
C)  62 
D)  66 
A)  102 
B)  72 
C)  62 
D)  66

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

Graph the cycloid for t in the indicated interval. - $x = 7 t - 7 \sin t , y = 7 - 7 \cos t , - 2 \pi \leq t \leq 2 \pi$ $Graph the cycloid for t in the indicated interval. - x = 7 t - 7 \sin t , y = 7 - 7 \cos t , - 2 \pi \leq t \leq 2 \pi$

Write the complex number in trigonometric form $r ( \cos \theta + i \sin \theta )$ with θ in the interval [0°, 360°). - $- 6 - 6 \mathrm { i } \sqrt { 3 }$

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary. - =38. =12.0. =5.5.

Find all solutions of the equation. Leave answers in trigonometric form. - $x ^ { 4 } + 16 = 0$

Find all specified roots. -Cube roots of $i$ .

Write the complex number in rectangular form. - $3 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$

Solve the problem. -A solar reflector is made using 35 identical triangular-shaped mirrors, each having sides 2 meters, 1.7 meters, 1.5 meters. What is the total surface area of the reflector (to the nearest square meter)?

The rectangular coordinates of a point are given. Express the point in polar coordinates with r ≥ 0 and 0° ≤ θ < 360°. - $\left( \frac { 1 } { 3 } , \frac { \sqrt { 3 } } { 3 } \right)$

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

Find all cube roots of the complex number. Leave answers in trigonometric form. - $- 3 \sqrt { 3 } + 3 i$

Answer the question. -On which line do the square roots of $- \mathrm { i }$ lie?

Find the missing parts of the triangle. - =33 =18.76 =16.15 If necessary, round side lengths to the nearest hundredth.

Give the rectangular coordinates for the point. - $( 5 , \pi )$

Solve the problem. -A force of $670 \mathrm { lb }$ is required to pull a boat up a ramp inclined at $25 ^ { \circ }$ with the horizontal. How much does the boat weigh?

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

Give the rectangular coordinates for the point. - $\left( 2,90 ^ { \circ } \right)$

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations. - $x = t ^ { 2 } - 9 , y = t ^ { 2 } + 8 ; t = 3$

Solve the problem. -If $\mathbf { u } = \langle - 3,5 \rangle$ and $\mathbf { v } = \langle 4,9 \rangle$ , evaluate $( 2 \mathbf { u } ) \cdot \mathbf { v }$ .

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