Question 1

Give the rectangular coordinates for the point.
-$$\left( 5,150 ^ { \circ } \right)$$

Accepted Answer

A)  $\left( - \frac { 5 } { 2 } , \frac { 5 \sqrt { 3 } } { 2 } \right)$ 
B)  $\left( - \frac { 5 } { 2 } , \frac { - 5 \sqrt { 3 } } { 2 } \right)$ 
C)  $\left( \frac { - 5 \sqrt { 3 } } { 2 } , \frac { 5 } { 2 } \right)$ 
D)  $\left( \frac { 5 \sqrt { 3 } } { 2 } , - \frac { 5 } { 2 } \right)$ 
A)  $\left( - \frac { 5 } { 2 } , \frac { 5 \sqrt { 3 } } { 2 } \right)$ 
B)  $\left( - \frac { 5 } { 2 } , \frac { - 5 \sqrt { 3 } } { 2 } \right)$ 
C)  $\left( \frac { - 5 \sqrt { 3 } } { 2 } , \frac { 5 } { 2 } \right)$ 
D)  $\left( \frac { 5 \sqrt { 3 } } { 2 } , - \frac { 5 } { 2 } \right)$

Question 2

Find the missing parts of the triangle.
-$$\begin{array} { l } 
C = 90 ^ { \circ } \
c = 24 \mathrm {~m} \
\mathrm { a } = 48 \mathrm {~m}
\end{array}$$
If necessary, round angles to the nearest degree and give exact values of side lengths.

Accepted Answer

A)  $A = 30 ^ { \circ } , B = 60 ^ { \circ } , b = 24 \sqrt { 3 } \mathrm {~m}$ 
B)  $A = 30 ^ { \circ } , B = 60 ^ { \circ } , b = 24 \sqrt { 2 } \mathrm {~m}$ 
C)  no such triangle 
D)  $A = 60 ^ { \circ } , B = 30 ^ { \circ } , b = 24 \sqrt { 3 } \mathrm {~m}$ 
A)  $A = 30 ^ { \circ } , B = 60 ^ { \circ } , b = 24 \sqrt { 3 } \mathrm {~m}$ 
B)  $A = 30 ^ { \circ } , B = 60 ^ { \circ } , b = 24 \sqrt { 2 } \mathrm {~m}$ 
C)  no such triangle 
D)  $A = 60 ^ { \circ } , B = 30 ^ { \circ } , b = 24 \sqrt { 3 } \mathrm {~m}$

Question 3

Graph the complex number.
-3i

Accepted Answer

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

Question 4

Give the rectangular coordinates for the point.
-$\left( - 10,225 ^ { \circ } \right)$

Accepted Answer

A)  $( 5 \sqrt { 2 } , 5 )$ 
B)  $( - 5 , - 5 \sqrt { 2 } )$ 
C)  $( 5 \sqrt { 2 } , 5 \sqrt { 2 } )$ 
D)  $( - 5 \sqrt { 2 } , - 5 )$ 
A)  $( 5 \sqrt { 2 } , 5 )$ 
B)  $( - 5 , - 5 \sqrt { 2 } )$ 
C)  $( 5 \sqrt { 2 } , 5 \sqrt { 2 } )$ 
D)  $( - 5 \sqrt { 2 } , - 5 )$

Question 5

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

Question 6

Given that the polar equation r models the orbits of the planets about the sun,
-Suppose that a radio transmission pattern can be modeled by $$r ^ { 2 } = 16,900 \sin 2 \theta , \text { for } 0 ^ { \circ } \leq \theta \leq 360 ^ { \circ } \text {, }$$ 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 and southwest; 16,900 miles 
B)  Northeast; 130 miles 
C)  Northeast and southwest; 130 miles 
D)  North and south; 130 miles 
A)  Northeast and southwest; 16,900 miles 
B)  Northeast; 130 miles 
C)  Northeast and southwest; 130 miles 
D)  North and south; 130 miles

Question 7

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

Accepted Answer

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

Question 8

Write the vector in the form ai + bj.
--2, 9

Accepted Answer

A)  -2i + 9j 
B)  2i + 9j 
C)  9i - 2j 
D)  9i + 2j 
A)  -2i + 9j 
B)  2i + 9j 
C)  9i - 2j 
D)  9i + 2j

Question 9

Write the complex number in trigonometric form r(c $$r ( \cos \theta + i \sin \theta )$$ ), with $$\theta$$ in the interval [0 $$\left[ 0 ^ { \circ } , 360 ^ { \circ } \right)$$
-$3 \sqrt { 3 } + 3 i$

Accepted Answer

A)  $6 \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right)$ 
B)  $6 \left( \cos 60 ^ { \circ } + i \sin 60 ^ { \circ } \right)$ 
C)  $6 \left( \cos 150 ^ { \circ } + i \sin 150 ^ { \circ } \right)$ 
D)  $6 \left( \cos 330 ^ { \circ } + i \sin 330 ^ { \circ } \right)$ 
A)  $6 \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right)$ 
B)  $6 \left( \cos 60 ^ { \circ } + i \sin 60 ^ { \circ } \right)$ 
C)  $6 \left( \cos 150 ^ { \circ } + i \sin 150 ^ { \circ } \right)$ 
D)  $6 \left( \cos 330 ^ { \circ } + i \sin 330 ^ { \circ } \right)$

Question 10

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.
-A solar reflector is made using 32 identical triangular-shaped mirrors, each having sides $1.7$ meters, $2.3$ meters, $1.4$ meters. What is the total surface area of the reflector (to the nearest square meter)?

Accepted Answer

A)  $45 m ^ { 2 }$ 
B)  $38 \mathrm {~m} ^ { 2 }$ 
C)  $35 \mathrm {~m} ^ { 2 }$ 
D)  $33 \mathrm {~m} ^ { 2 }$ 
A)  $45 m ^ { 2 }$ 
B)  $38 \mathrm {~m} ^ { 2 }$ 
C)  $35 \mathrm {~m} ^ { 2 }$ 
D)  $33 \mathrm {~m} ^ { 2 }$

Question 11

Write the complex number in rectangular form.
-$10 \operatorname { cis } 135 ^ { \circ }$

Accepted Answer

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

Question 12

Find all cube roots of the complex number. Leave answers in trigonometric form.
-$64 \left( \cos 237 ^ { \circ } + \mathrm { i } \sin 237 ^ { \circ } \right)$

Accepted Answer

A)  $4 \operatorname { cis } 79 ^ { \circ } , 4 \operatorname { cis } 139 ^ { \circ } , 4 \operatorname { cis } 19 ^ { \circ }$ 
B)  $4 \operatorname { cis } 79 ^ { \circ } , 4 \operatorname { cis } 199 ^ { \circ } , 4 \operatorname { cis } 319 ^ { \circ }$ 
C)  $4 \operatorname { cis } 169 ^ { \circ } , 4 \operatorname { cis } 229 ^ { \circ } , 4 \operatorname { cis } 109 ^ { \circ }$ 
D)  $4 \operatorname { cis } 79 ^ { \circ } , 4 \operatorname { cis } 199 ^ { \circ } , 4 \operatorname { cis } 199 ^ { \circ }$ 
A)  $4 \operatorname { cis } 79 ^ { \circ } , 4 \operatorname { cis } 139 ^ { \circ } , 4 \operatorname { cis } 19 ^ { \circ }$ 
B)  $4 \operatorname { cis } 79 ^ { \circ } , 4 \operatorname { cis } 199 ^ { \circ } , 4 \operatorname { cis } 319 ^ { \circ }$ 
C)  $4 \operatorname { cis } 169 ^ { \circ } , 4 \operatorname { cis } 229 ^ { \circ } , 4 \operatorname { cis } 109 ^ { \circ }$ 
D)  $4 \operatorname { cis } 79 ^ { \circ } , 4 \operatorname { cis } 199 ^ { \circ } , 4 \operatorname { cis } 199 ^ { \circ }$

Question 13

Solve the problem.
-A projectile is fired with an initial velocity of 450 feet per second at an angle of 45° with the horizontal. To the nearest foot, find the maximum altitude of the projectile.

Accepted Answer

A)  1598 ft 
B)  1574 ft 
C)  1565 ft 
D)  1582 ft 
A)  1598 ft 
B)  1574 ft 
C)  1565 ft 
D)  1582 ft

Question 14

Find all cube roots of the complex number. Leave answers in trigonometric form.
-$64 \operatorname { cis } 120 ^ { \circ }$

Accepted Answer

A)  $4 ( .6428 + .7660 \mathrm { i } ) , 4 ( - .3420 + .9397 \mathrm { i } ) , 4 ( .9848 - .1736 \mathrm { i } )$ 
B)  $4 \left( - \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } \mathrm { i } \right)$, $4 \left( \frac { 1 } { 2 } \mathrm { i } - \frac { \sqrt { 3 } } { 2 } \right) , 4 \left( \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } \mathrm { i } \right)$ 
C)  $4 \left( \frac { \sqrt { 3 } } { 2 } + \frac { 1 } { 2 } \mathrm { i } \right) , 4 \left( - \frac { \sqrt { 3 } } { 2 } + \frac { 1 } { 2 } \mathrm { i } \right) , 4 \left( \frac { \sqrt { 3 } } { 2 } - \frac { 1 } { 2 } \mathrm { i } \right)$ 
D)  $4 ( .7660 + .6428 \mathrm { i } ) , 4 ( - .9397 + .3420 \mathrm { i } ) , 4 ( .1736 - .9848 \mathrm { i } )$ 
A)  $4 ( .6428 + .7660 \mathrm { i } ) , 4 ( - .3420 + .9397 \mathrm { i } ) , 4 ( .9848 - .1736 \mathrm { i } )$ 
B)  $4 \left( - \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } \mathrm { i } \right)$, $4 \left( \frac { 1 } { 2 } \mathrm { i } - \frac { \sqrt { 3 } } { 2 } \right) , 4 \left( \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } \mathrm { i } \right)$ 
C)  $4 \left( \frac { \sqrt { 3 } } { 2 } + \frac { 1 } { 2 } \mathrm { i } \right) , 4 \left( - \frac { \sqrt { 3 } } { 2 } + \frac { 1 } { 2 } \mathrm { i } \right) , 4 \left( \frac { \sqrt { 3 } } { 2 } - \frac { 1 } { 2 } \mathrm { i } \right)$ 
D)  $4 ( .7660 + .6428 \mathrm { i } ) , 4 ( - .9397 + .3420 \mathrm { i } ) , 4 ( .1736 - .9848 \mathrm { i } )$

Question 15

Answer the question.
-If $\mathrm { n }$ is an even number, then which of the following statements is true?

Accepted Answer

A)  The equation $x ^ { n } - 1 = 0$ has exactly two real roots. 
B)  The equation $x ^ { n } - 1 = 0$ has an odd number of nonreal roots. 
C)  The equation $x ^ { n } - 1 = 0$ has an odd number of real roots. 
D)  The equation $x ^ { n } - 1 = 0$ has $n - 1$ roots. 
A)  The equation $x ^ { n } - 1 = 0$ has exactly two real roots. 
B)  The equation $x ^ { n } - 1 = 0$ has an odd number of nonreal roots. 
C)  The equation $x ^ { n } - 1 = 0$ has an odd number of real roots. 
D)  The equation $x ^ { n } - 1 = 0$ has $n - 1$ roots.

Question 16

Solve the problem.
-It is $4.7 \mathrm {~km}$ from Lighthouse A to Port B. The bearing of the port from the lighthouse is N73${ } ^ { \circ } \mathrm { E }$. A ship has sailed due west from the port and its bearing from the lighthouse is $N 31 ^ { \circ } \mathrm { E }$. How far has the ship sailed from the port? Round to the nearest tenth of a kilometer.

Accepted Answer

A)  $2.7 \mathrm {~km}$ 
B)  $3.1 \mathrm {~km}$ 
C)  $3.7 \mathrm {~km}$ 
D)  $3.5 \mathrm {~km}$ 
A)  $2.7 \mathrm {~km}$ 
B)  $3.1 \mathrm {~km}$ 
C)  $3.7 \mathrm {~km}$ 
D)  $3.5 \mathrm {~km}$

Question 17

The graph o $$r = a \theta$$ in polar coordinates is an example of the spiral of Archimedes. With your calculator set to radian
mode, use the given value of a and interval of  to graph the spiral in the window specified.
-$$\mathrm { a } = 3,0 \leq \theta \leq 2 \pi , [ - 20,20 ] \text { by } [ - 20,20 ]$$

Accepted Answer

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

Question 18

Perform the indicated operation. Give answers in rectangular form expressing real and imaginary parts to four decimal
places.
-The current $I$ in a circuit with voltage $E$, resistance $R$, capacitive reactance $X _ { C }$ and inductive reactance $\mathrm { X } _ { \mathrm { L } }$ is
$$I = \frac { E } { R + \left( X _ { L } - X _ { C } \right) i }$$
Find $I$ if $E = 3 \sqrt { 2 } \left( \cos 45 ^ { \circ } + i \sin 45 ^ { \circ } \right) , R = 5 , X _ { L } = 6$, and $X _ { C } = 4$.
Give your answer in rectangular form.

Accepted Answer

A)  $\frac { 9 } { 29 } + \frac { 21 } { 29 } \mathrm { i }$ 
B)  $\frac { 21 } { 29 } + \frac { 9 } { 29 } \mathrm { i }$ 
C)  $\frac { 21 } { 29 } + \frac { 21 } { 29 } \mathrm { i }$ 
D)  $\frac { 9 } { 29 } + \frac { 9 } { 29 } \mathrm { i }$ 
A)  $\frac { 9 } { 29 } + \frac { 21 } { 29 } \mathrm { i }$ 
B)  $\frac { 21 } { 29 } + \frac { 9 } { 29 } \mathrm { i }$ 
C)  $\frac { 21 } { 29 } + \frac { 21 } { 29 } \mathrm { i }$ 
D)  $\frac { 9 } { 29 } + \frac { 9 } { 29 } \mathrm { i }$

Question 19

Find all specified roots.
-Fifth roots of i.

Accepted Answer

A)  $\operatorname { cis } \frac { \pi } { 10 } , i , \operatorname { cis } \frac { 9 \pi } { 10 } , \operatorname { cis } \frac { 13 \pi } { 10 } , \operatorname { cis } \frac { 17 \pi } { 10 }$ 
B)  $\operatorname { cis } \frac { \pi } { 5 } , \operatorname { cis } \frac { 3 \pi } { 5 } , - 1 , \operatorname { cis } \frac { 7 \pi } { 10 } , \operatorname { cis } \frac { 9 \pi } { 10 }$ 
C)  $\operatorname { cis } \frac { 2 \pi } { 5 } , \operatorname { cis } \frac { 4 \pi } { 5 } , \operatorname { cis } \frac { 6 \pi } { 5 } , \operatorname { cis } \frac { 8 \pi } { 10 } , 1$ 
D)  $\operatorname { cis } \frac { \pi } { 10 } , \operatorname { cis } \frac { 7 \pi } { 10 } , \operatorname { cis } \frac { 9 \pi } { 10 } , \operatorname { cis } \frac { 13 \pi } { 10 } , \operatorname { cis } \frac { 17 \pi } { 10 }$ 
A)  $\operatorname { cis } \frac { \pi } { 10 } , i , \operatorname { cis } \frac { 9 \pi } { 10 } , \operatorname { cis } \frac { 13 \pi } { 10 } , \operatorname { cis } \frac { 17 \pi } { 10 }$ 
B)  $\operatorname { cis } \frac { \pi } { 5 } , \operatorname { cis } \frac { 3 \pi } { 5 } , - 1 , \operatorname { cis } \frac { 7 \pi } { 10 } , \operatorname { cis } \frac { 9 \pi } { 10 }$ 
C)  $\operatorname { cis } \frac { 2 \pi } { 5 } , \operatorname { cis } \frac { 4 \pi } { 5 } , \operatorname { cis } \frac { 6 \pi } { 5 } , \operatorname { cis } \frac { 8 \pi } { 10 } , 1$ 
D)  $\operatorname { cis } \frac { \pi } { 10 } , \operatorname { cis } \frac { 7 \pi } { 10 } , \operatorname { cis } \frac { 9 \pi } { 10 } , \operatorname { cis } \frac { 13 \pi } { 10 } , \operatorname { cis } \frac { 17 \pi } { 10 }$

Question 20

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.
-$$\begin{array} { l } 
\mathrm { A } = 31 ^ { \circ } 40 ^ { \prime } \
\mathrm { b } = 19.3 \mathrm {~m} \
\mathrm { c } = 7.9 \mathrm {~m}
\end{array}$$

Accepted Answer

A)  $20 \mathrm {~m} ^ { 2 }$ 
B)  $80 \mathrm {~m} ^ { 2 }$ 
C)  $40 \mathrm {~m} ^ { 2 }$ 
D)  $82 \mathrm {~m} ^ { 2 }$ 
A)  $20 \mathrm {~m} ^ { 2 }$ 
B)  $80 \mathrm {~m} ^ { 2 }$ 
C)  $40 \mathrm {~m} ^ { 2 }$ 
D)  $82 \mathrm {~m} ^ { 2 }$

Give the rectangular coordinates for the point. - $\left( 5,150 ^ { \circ } \right)$

Find the missing parts of the triangle. - C=9 c=24 =48 If necessary, round angles to the nearest degree and give exact values of side lengths.

Graph the complex number. -3i

Give the rectangular coordinates for the point. - $\left( - 10,225 ^ { \circ } \right)$

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

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

Write the vector in the form ai + bj. --2, 9

Write the complex number in trigonometric form r(c $r ( \cos \theta + i \sin \theta )$ ), with $\theta$ in the interval [0 $\left[ 0 ^ { \circ } , 360 ^ { \circ } \right)$ - $3 \sqrt { 3 } + 3 i$

Write the complex number in rectangular form. - $10 \operatorname { cis } 135 ^ { \circ }$

Find all cube roots of the complex number. Leave answers in trigonometric form. - $64 \left( \cos 237 ^ { \circ } + \mathrm { i } \sin 237 ^ { \circ } \right)$

Solve the problem. -A projectile is fired with an initial velocity of 450 feet per second at an angle of 45° with the horizontal. To the nearest foot, find the maximum altitude of the projectile.

Find all cube roots of the complex number. Leave answers in trigonometric form. - $64 \operatorname { cis } 120 ^ { \circ }$

Answer the question. -If $\mathrm { n }$ is an even number, then which of the following statements is true?

Find all specified roots. -Fifth roots of i.

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary. - =34 =19.3 =7.9

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

Give the rectangular coordinates for the point. - (5,150∘)\left( 5,150 ^ { \circ } \right)(5,150∘)