Question 1

Write the vector in the form ai + bj.
-7, 9

Accepted Answer

A)  9i + 7j 
B)  7i + 9j 
C)  9i - 7j 
D)  -7i + 9j 
A)  9i + 7j 
B)  7i + 9j 
C)  9i - 7j 
D)  -7i + 9j

Question 2

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.
-Two forces of 683 newtons and 274 newtons act at a point. The resultant force is 766 newtons. Find the angle between the forces.

Accepted Answer

A)  $96.9 ^ { \circ }$ 
B)  $163.4 ^ { \circ }$ 
C)  $83.1 ^ { \circ }$ 
D)  $136.3 ^ { \circ }$ 
A)  $96.9 ^ { \circ }$ 
B)  $163.4 ^ { \circ }$ 
C)  $83.1 ^ { \circ }$ 
D)  $136.3 ^ { \circ }$

Question 3

Given that the polar equation r models the orbits of the planets about the sun,
-Suppose that a radio signal transmission pattern can be modeled by $$\mathrm { r } ^ { 2 } = \mathrm { k } \cos 2 \theta \text {, for } 0 ^ { \circ } \leq \theta \leq 360 ^ { \circ } ,$$ where the units are in miles. Describe the influence of k on the pattern. Assume that the positive x-axis points east.

Accepted Answer

A)  With increasing k, the distance of transmission becomes smaller in the east and west directions. 
B)  With increasing k, the transmission becomes more strongly directed toward the east and less strongly directed to the west. 
C)  With increasing k, the distance of transmission becomes greater in the east and west directions. 
D)  With increasing k, the transmission becomes more strongly directed toward the north and less strongly directed to the east. 
A)  With increasing k, the distance of transmission becomes smaller in the east and west directions. 
B)  With increasing k, the transmission becomes more strongly directed toward the east and less strongly directed to the west. 
C)  With increasing k, the distance of transmission becomes greater in the east and west directions. 
D)  With increasing k, the transmission becomes more strongly directed toward the north and less strongly directed to the east.

Question 4

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

Accepted Answer

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

Question 5

Solve the problem.
-If u =-5, 7 , v =1, 6, and w =-11, 2 , evaluate u · (v - w).

Accepted Answer

A)  -37 
B)  -5 
C)  -28 
D)  -32 
A)  -37 
B)  -5 
C)  -28 
D)  -32

Question 6

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

Accepted Answer

A)  $\langle 37.28,44.43 \rangle$ 
B)  $\langle 44.43,37.28 \rangle$ 
C)  $\langle 41.01,41.01 \rangle$ 
D)  $\langle 0.64,0.7 \rangle \rangle$ 
A)  $\langle 37.28,44.43 \rangle$ 
B)  $\langle 44.43,37.28 \rangle$ 
C)  $\langle 41.01,41.01 \rangle$ 
D)  $\langle 0.64,0.7 \rangle \rangle$

Question 7

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.
-

Accepted Answer

A)  $21,459.5 \mathrm { lb }$ 
B)  $132.7 \mathrm { lb }$ 
C)  $180.3 \mathrm { lb }$ 
D)  $146.5 \mathrm { lb }$ 
A)  $21,459.5 \mathrm { lb }$ 
B)  $132.7 \mathrm { lb }$ 
C)  $180.3 \mathrm { lb }$ 
D)  $146.5 \mathrm { lb }$

Question 8

Vector v has the given magnitude and direction. Find the horizontal or vertical component of v, as indicated, if $\theta$ is the
direction angle of v from the horizontal. Round to the nearest tenth when necessary.
-$\alpha = 33.9 ^ { \circ } , | \mathbf { v } | = 82.9 ;$ Find the horizontal component of $\mathbf { v }$

Accepted Answer

A)  $46.2$ 
B)  $22.6$ 
C)  115 
D)  $68.8$ 
A)  $46.2$ 
B)  $22.6$ 
C)  115 
D)  $68.8$

Question 9

Is the given number z in the Julia set?
-z = -1 + 1i

Accepted Answer

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

Question 10

Use a table of values to graph the plane curve defined by the following parametric equations. Find a rectangular equation
for the curve.
-$x = t ^ { 3 } + 1 , y = t ^ { 3 } - 1$, for $t$ in $[ - 2,2 ]$

Accepted Answer

A) 
 
$$y = - x ^ { 2 } \text {, for } x \text { in } [ - 4,4 ]$$ 
B) 
 
$$y = - x - 2 , \text { for } x \text { in } [ - 7,9 ]$$ 
C) 
 
$$y = x ^ { 3 } , \text { for } x \text { in } [ - 3,1 ]$$ 
D) 
 
$$y = x - 2 , \text { for } x \text { in } [ - 7,9 ]$$ 
A) 
 
$$y = - x ^ { 2 } \text {, for } x \text { in } [ - 4,4 ]$$ 
B) 
 
$$y = - x - 2 , \text { for } x \text { in } [ - 7,9 ]$$ 
C) 
 
$$y = x ^ { 3 } , \text { for } x \text { in } [ - 3,1 ]$$ 
D) 
 
$$y = x - 2 , \text { for } x \text { in } [ - 7,9 ]$$

Question 11

Solve the problem.
-If u =-5, 7 , v =2, 6, and w =-11, 2 , evaluate u ·v - u ·w.

Accepted Answer

A)  -33 
B)  -37 
C)  -10 
D)  -42 
A)  -33 
B)  -37 
C)  -10 
D)  -42

Question 12

Determine the number of triangles ABC possible with the given parts.
-$$a = 38 , b = 77 , A = 74 ^ { \circ }$$

Accepted Answer

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

Question 13

Solve the problem.
-A projectile is fired with an initial velocity of 600 feet per second at an angle of 45° 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)  31.3 sec 
B)  34.6 sec 
C)  23.1 sec 
D)  26.5 sec 
A)  31.3 sec 
B)  34.6 sec 
C)  23.1 sec 
D)  26.5 sec

Question 14

Find the missing parts of the triangle.
-$$\begin{array} { l } 
\mathrm { A } = 30 ^ { \circ } \
\mathrm { a } = 9.32 \
\mathrm {~b} = 18.64
\end{array}$$
If necessary, round angles to the nearest degree and side lengths to the nearest hundredth.

Accepted Answer

A)  no such triangle 
B)  $\mathrm { B } = 90 ^ { \circ } , \mathrm { C } = 60 ^ { \circ } , \mathrm { c } = 16.14$ 
C)  $\mathrm { B } = 60 ^ { \circ } , \mathrm { C } = 60 ^ { \circ } , \mathrm { c } = 16.14$ 
D)  $\mathrm { B } = 60 ^ { \circ } , \mathrm { C } = 90 ^ { \circ } , \mathrm { c } = 16.14$ 
A)  no such triangle 
B)  $\mathrm { B } = 90 ^ { \circ } , \mathrm { C } = 60 ^ { \circ } , \mathrm { c } = 16.14$ 
C)  $\mathrm { B } = 60 ^ { \circ } , \mathrm { C } = 60 ^ { \circ } , \mathrm { c } = 16.14$ 
D)  $\mathrm { B } = 60 ^ { \circ } , \mathrm { C } = 90 ^ { \circ } , \mathrm { c } = 16.14$

Question 15

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as
an angle in $$\left[ 0,360 ^ { \circ } \right]$$
-$$\langle - 9 \sqrt { 2 } , - 9 \sqrt { 2 } \rangle$$

Accepted Answer

A)  $18 \sqrt { 2 } ; 135 ^ { \circ }$ 
B)  $36 ; 45 ^ { \circ }$ 
C)  $18 ; 225 ^ { \circ }$ 
D)  $18 ; 45 ^ { \circ }$ 
A)  $18 \sqrt { 2 } ; 135 ^ { \circ }$ 
B)  $36 ; 45 ^ { \circ }$ 
C)  $18 ; 225 ^ { \circ }$ 
D)  $18 ; 45 ^ { \circ }$

Question 16

Solve the problem.
-A guy wire to a tower makes a $70 ^ { \circ }$ angle with level ground. At a point $32 \mathrm { ft }$ farther from the tower than the wire but on the same side of the base as the wire, the angle of elevation to the top of the pole is $39 ^ { \circ }$. Find the wire length (to the nearest foot).

Accepted Answer

A)  $44 \mathrm { ft }$ 
B)  $83 \mathrm { ft }$ 
C)  $39 \mathrm { ft }$ 
D)  $78 \mathrm { ft }$ 
A)  $44 \mathrm { ft }$ 
B)  $83 \mathrm { ft }$ 
C)  $39 \mathrm { ft }$ 
D)  $78 \mathrm { ft }$

Question 17

Find all specified roots.
-Cube roots of 1 .

Accepted Answer

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

Question 18

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form.
-$$\frac { \sqrt { 3 } ( \cos 315 + i \sin 315 ) } { \sqrt { 6 } ( \cos 45 + i \sin 45 ) }$$

Accepted Answer

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

Question 19

Give the rectangular coordinates for the point.
-$$\left( 8,225 ^ { \circ } \right)$$

Accepted Answer

A)  $( - 4 \pi , - 4 \pi )$ 
B)  $( - 4 \sqrt { 3 } , - 4 \sqrt { 3 } )$ 
C)  $( - 4 \sqrt { 2 } , - 4 \sqrt { 2 } )$ 
D)  $( 4 \sqrt { 2 } , 4 \sqrt { 2 } )$ 
A)  $( - 4 \pi , - 4 \pi )$ 
B)  $( - 4 \sqrt { 3 } , - 4 \sqrt { 3 } )$ 
C)  $( - 4 \sqrt { 2 } , - 4 \sqrt { 2 } )$ 
D)  $( 4 \sqrt { 2 } , 4 \sqrt { 2 } )$

Question 20

Find a rectangular equation for the plane curve defined by the parametric equations.
-$x = t ^ { 2 } + 1 , y = t ^ { 2 } - 1$

Accepted Answer

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

Write the vector in the form ai + bj. -7, 9

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. -Two forces of 683 newtons and 274 newtons act at a point. The resultant force is 766 newtons. Find the angle between the forces.

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

Solve the problem. -If u =-5, 7 , v =1, 6, and w =-11, 2 , evaluate u · (v - w).

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

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. -

Is the given number z in the Julia set? -z = -1 + 1i

Solve the problem. -If u =-5, 7 , v =2, 6, and w =-11, 2 , evaluate u ·v - u ·w.

Determine the number of triangles ABC possible with the given parts. - $a = 38 , b = 77 , A = 74 ^ { \circ }$

Solve the problem. -A projectile is fired with an initial velocity of 600 feet per second at an angle of 45° with the horizontal. In how many seconds will the projectile strike the ground? (Round your answer to the Nearest tenth of a second.)

Find the missing parts of the triangle. - =3 =9.32 =18.64 If necessary, round angles to the nearest degree and side lengths to the nearest hundredth.

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in $\left[ 0,360 ^ { \circ } \right]$ - $\langle - 9 \sqrt { 2 } , - 9 \sqrt { 2 } \rangle$

Find all specified roots. -Cube roots of 1 .

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - $\frac { \sqrt { 3 } ( \cos 315 + i \sin 315 ) } { \sqrt { 6 } ( \cos 45 + i \sin 45 ) }$

Give the rectangular coordinates for the point. - $\left( 8,225 ^ { \circ } \right)$

Find a rectangular equation for the plane curve defined by the parametric equations. - $x = t ^ { 2 } + 1 , y = t ^ { 2 } - 1$

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