Question 1

Find the missing parts of the triangle.
-$$\begin{array} { l } 
\mathrm { A } = 118.6 ^ { \circ } \
a = 1263 \mathrm {~cm} \
b = 1363 \mathrm {~cm}
\end{array}$$
If necessary, round angles to the nearest tenth and side lengths to the nearest $\mathrm { cm }$.

Accepted Answer

A)  $\mathrm { B } = 36.7 ^ { \circ } , \mathrm { C } = 24.7 ^ { \circ } , \mathrm { c } = 1023 \mathrm {~cm}$ 
B)  no such triangle 
C)  $B = 32.8 ^ { \circ } , C = 28.6 ^ { \circ } , \mathrm { c } = 1023 \mathrm {~cm}$ 
D)  $B = 24.7 ^ { \circ } , C = 36.7 ^ { \circ } , c = 1023 \mathrm {~cm}$ 
A)  $\mathrm { B } = 36.7 ^ { \circ } , \mathrm { C } = 24.7 ^ { \circ } , \mathrm { c } = 1023 \mathrm {~cm}$ 
B)  no such triangle 
C)  $B = 32.8 ^ { \circ } , C = 28.6 ^ { \circ } , \mathrm { c } = 1023 \mathrm {~cm}$ 
D)  $B = 24.7 ^ { \circ } , C = 36.7 ^ { \circ } , c = 1023 \mathrm {~cm}$

Question 2

Give the rectangular coordinates for the point.
-$$\left( 3 , - \frac { \pi } { 3 } \right)$$

Accepted Answer

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

Question 3

Find the dot product for the pair of vectors.
--15, 10, 0, 8

Accepted Answer

A)  -120 
B)  65 
C)  95 
D)  80 
A)  -120 
B)  65 
C)  95 
D)  80

Question 4

Write the complex number in rectangular form.
-$$8 \left( \cos \frac { \pi } { 6 } + i \sin \frac { \pi } { 6 } \right)$$

Accepted Answer

A)  $\frac { 1 } { 4 } + \frac { \sqrt { 3 } } { 4 }$ i 
B)  $\frac { \sqrt { 3 } } { 4 } + \frac { 1 } { 4 } \mathrm { i }$ 
C)  $4 + 4 \sqrt { 3 } i$ 
D)  $4 \sqrt { 3 } + 4 i$ 
A)  $\frac { 1 } { 4 } + \frac { \sqrt { 3 } } { 4 }$ i 
B)  $\frac { \sqrt { 3 } } { 4 } + \frac { 1 } { 4 } \mathrm { i }$ 
C)  $4 + 4 \sqrt { 3 } i$ 
D)  $4 \sqrt { 3 } + 4 i$

Question 5

The rectangular coordinates of a point are given. Express the point in polar coordinates with $$r \geq 0 \text { and } 0 ^ { \circ } \leq \theta < 360 ^ { \circ } \text {. }$$
-$$\left( \frac { 1 } { 3 } , \frac { - \sqrt { 3 } } { 3 } \right)$$

Accepted Answer

A)  $\left( \frac { 2 } { 3 } , 300 ^ { \circ } \right)$ 
B)  $\left( \frac { 2 } { 3 } , 60 ^ { \circ } \right)$ 
C)  $\left[ \frac { 1 } { 3 } , 150 ^ { \circ } \right)$ 
D)  $\left( \frac { 2 } { 3 } , 30 ^ { \circ } \right)$ 
A)  $\left( \frac { 2 } { 3 } , 300 ^ { \circ } \right)$ 
B)  $\left( \frac { 2 } { 3 } , 60 ^ { \circ } \right)$ 
C)  $\left[ \frac { 1 } { 3 } , 150 ^ { \circ } \right)$ 
D)  $\left( \frac { 2 } { 3 } , 30 ^ { \circ } \right)$

Question 6

Assume a triangle ABC has standard labeling. Determine whether SAA, ASA, SSA, SAS, or SSS is given. Then decide
whether the law of sines or the law of cosines should be used to begin solving the triangle.
-a, c, and B

Accepted Answer

A)  SAS; law of sines 
B)  SSA; law of sines 
C)  SAS; law of cosines 
D)  SSA; law of cosines 
A)  SAS; law of sines 
B)  SSA; law of sines 
C)  SAS; law of cosines 
D)  SSA; law of cosines

Question 7

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

Accepted Answer

A)

$y = x ^ { 2 } + 1$, for $x$ in $[ - 2,2 ]$ 
B)

$y = \frac { 1 } { 3 } x + 1$, for $x$ in $[ - 6,9 ]$ 
C) 
 
$y = - 3 x + 1$, for $x$ in $[ - 9,6 ]$ 
D)

$y = \frac { 1 } { 3 } x - 1$, for $x$ in $[ - 6,9 ]$ 
A)

$y = x ^ { 2 } + 1$, for $x$ in $[ - 2,2 ]$ 
B)

$y = \frac { 1 } { 3 } x + 1$, for $x$ in $[ - 6,9 ]$ 
C) 
 
$y = - 3 x + 1$, for $x$ in $[ - 9,6 ]$ 
D)

$y = \frac { 1 } { 3 } x - 1$, for $x$ in $[ - 6,9 ]$

Question 8

Determine the number of triangles ABC possible with the given parts.
-$$b = 24 , c = 29 , B = 46 ^ { \circ }$$

Accepted Answer

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

Question 9

Find the missing parts of the triangle.
-$$\begin{array} { l } 
\mathrm { B } = 106.3 ^ { \circ } \
\mathrm { a } = 298 \mathrm {~cm} \
\mathrm {~b} = 1353 \mathrm {~cm}
\end{array}$$
If necessary, round angles the nearest tenth and side lengths to the nearest $\mathrm { cm }$.

Accepted Answer

A)  $\mathrm { A } = 12.2 ^ { \circ } , \mathrm { C } = 61.5 ^ { \circ } , \mathrm { c } = 1239 \mathrm {~cm}$ 
B)  $\mathrm { A } = 61.5 ^ { \circ } , \mathrm { C } = 12.2 ^ { \circ } , \mathrm { c } = 1239 \mathrm {~cm}$ 
C)  no such triangle 
D)  $\mathrm { A } = 15.2 ^ { \circ } , \mathrm { C } = 58.5 ^ { \circ } , \mathrm { c } = 1239 \mathrm {~cm}$ 
A)  $\mathrm { A } = 12.2 ^ { \circ } , \mathrm { C } = 61.5 ^ { \circ } , \mathrm { c } = 1239 \mathrm {~cm}$ 
B)  $\mathrm { A } = 61.5 ^ { \circ } , \mathrm { C } = 12.2 ^ { \circ } , \mathrm { c } = 1239 \mathrm {~cm}$ 
C)  no such triangle 
D)  $\mathrm { A } = 15.2 ^ { \circ } , \mathrm { C } = 58.5 ^ { \circ } , \mathrm { c } = 1239 \mathrm {~cm}$

Question 10

Find an equivalent equation in rectangular coordinates.
-$$r = \frac { 2 } { 4 \sin \theta + 6 \cos \theta }$$

Accepted Answer

A)  $4 y + 6 x = 2$ 
B)  $4 y + 6 x = \frac { 2 } { \sqrt { x ^ { 2 } + y ^ { 2 } } }$ 
C)  $4 x - 6 y = 4$ 
D)  $4 x + 6 y = 2$ 
A)  $4 y + 6 x = 2$ 
B)  $4 y + 6 x = \frac { 2 } { \sqrt { x ^ { 2 } + y ^ { 2 } } }$ 
C)  $4 x - 6 y = 4$ 
D)  $4 x + 6 y = 2$

Question 11

Write the complex number in rectangular form.
-$$6 \left( \cos 330 ^ { \circ } + i \sin 330 ^ { \circ } \right)$$

Accepted Answer

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

Question 12

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

Accepted Answer

A)  $r = 8 \cos \theta$ 
B)  $r = 4 + \cos \theta$ 
C)  $r = 8 \sin \theta$ 
D)  $r = 4 + \sin \theta$ 
A)  $r = 8 \cos \theta$ 
B)  $r = 4 + \cos \theta$ 
C)  $r = 8 \sin \theta$ 
D)  $r = 4 + \sin \theta$

Question 13

Two forces act at a point in the plane. The angle between the two forces is given. Find the magnitude of the resultant
force.
-forces of 40 and 86 newtons, forming an angle of $90 ^ { \circ }$ (round to the nearest newton)

Accepted Answer

A)  95 newtons 
B)  46 newtons 
C)  126 newtons 
D)  3440 newtons 
A)  95 newtons 
B)  46 newtons 
C)  126 newtons 
D)  3440 newtons

Question 14

Find the indicated vector.
-Let $\mathbf { u } = 3 \mathbf { i } , \mathbf { v } = \mathbf { i } + \mathbf { j }$. Find $6 \mathbf { u } + \mathbf { v }$

Accepted Answer

A)  $19 \mathbf { i } + 6 \mathbf { j }$ 
B)  $\mathbf { i } + 19 \mathbf { j }$ 
C)  $19 i + j$ 
D)  $11 \mathbf { i } + \mathbf { j }$ 
A)  $19 \mathbf { i } + 6 \mathbf { j }$ 
B)  $\mathbf { i } + 19 \mathbf { j }$ 
C)  $19 i + j$ 
D)  $11 \mathbf { i } + \mathbf { j }$

Question 15

Find all solutions of the equation. Leave answers in trigonometric form.
-$$x ^ { 3 } + 8 i = 0$$

Accepted Answer

A)  $\left\{ 2 \operatorname { cis } 270 ^ { \circ } , 2 \right.$ cis $\left. 210 ^ { \circ } , 2 \operatorname { cis } 150 ^ { \circ } \right\}$ 
B)  $\left\{ 2 \operatorname { cis } 90 ^ { \circ } , 2 \right.$ cis $210 ^ { \circ } , 2$ cis $\left. 330 ^ { \circ } \right\}$ 
C)  $\left\{ 2 \operatorname { cis } 270 ^ { \circ } , 2 \right.$ cis $30 ^ { \circ } , 2$ cis $\left. 150 ^ { \circ } \right\}$ 
D)  $\left\{ 2 \operatorname { cis } 90 ^ { \circ } , 2 \right.$ cis $150 ^ { \circ } , 2$ cis $\left. 30 ^ { \circ } \right\}$ 
A)  $\left\{ 2 \operatorname { cis } 270 ^ { \circ } , 2 \right.$ cis $\left. 210 ^ { \circ } , 2 \operatorname { cis } 150 ^ { \circ } \right\}$ 
B)  $\left\{ 2 \operatorname { cis } 90 ^ { \circ } , 2 \right.$ cis $210 ^ { \circ } , 2$ cis $\left. 330 ^ { \circ } \right\}$ 
C)  $\left\{ 2 \operatorname { cis } 270 ^ { \circ } , 2 \right.$ cis $30 ^ { \circ } , 2$ cis $\left. 150 ^ { \circ } \right\}$ 
D)  $\left\{ 2 \operatorname { cis } 90 ^ { \circ } , 2 \right.$ cis $150 ^ { \circ } , 2$ cis $\left. 30 ^ { \circ } \right\}$

Question 16

Determine whether the pair of vectors is orthogonal.
-3i - 6j, -6i + 3j

Accepted Answer

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

Question 17

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 ship leaves point $A$ and travels directly north to point $B$. From point $B$, the ship then travels due east to point $\mathrm { C }$. The magnitude of the vector from point $\mathrm { A }$ to point $\mathrm { C }$ is 128 . Find the magnitude of the northern vector. Find the magnitude of the eastern vector.

Accepted Answer

A)  $64 \sqrt { 3 }$ north; 64 east 
B)  $64 \sqrt { 2 }$ north; $64 \sqrt { 2 }$ east 
C)  64 north; $64 \sqrt { 3 }$ east 
D)  64 north; 64 east 
A)  $64 \sqrt { 3 }$ north; 64 east 
B)  $64 \sqrt { 2 }$ north; $64 \sqrt { 2 }$ east 
C)  64 north; $64 \sqrt { 3 }$ east 
D)  64 north; 64 east

Question 18

Determine the number of triangles ABC possible with the given parts.
-$$\mathrm { a } = 24 , \mathrm {~b} = 19 , \mathrm {~A} = 43 ^ { \circ }$$

Accepted Answer

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

Question 19

Two forces act at a point in the plane. The angle between the two forces is given. Find the magnitude of the resultant
force.
-forces of $63.6$ and $45.0 \mathrm { lb }$, forming an angle of $98.5 ^ { \circ }$ (round to the nearest pound)

Accepted Answer

A)  $83 \mathrm { lb }$ 
B)  $6916 \mathrm { lb }$ 
C)  $72 \mathrm { lb }$ 
D)  $108 \mathrm { lb }$ 
A)  $83 \mathrm { lb }$ 
B)  $6916 \mathrm { lb }$ 
C)  $72 \mathrm { lb }$ 
D)  $108 \mathrm { lb }$

Question 20

Solve the problem.
-A projectile is fired with an initial velocity of 450 feet per second at an angle of 70° with the horizontal. In how many seconds will the projectile reach its maximum altitude? (Round your
Answer to the nearest tenth of a second.)

Accepted Answer

A)  21.3 sec 
B)  9.8 sec 
C)  18 sec 
D)  13.2 sec 
A)  21.3 sec 
B)  9.8 sec 
C)  18 sec 
D)  13.2 sec

Find the missing parts of the triangle. - =118. a=1263 b=1363 If necessary, round angles to the nearest tenth and side lengths to the nearest $\mathrm { cm }$ .

Give the rectangular coordinates for the point. - $\left( 3 , - \frac { \pi } { 3 } \right)$

Find the dot product for the pair of vectors. --15, 10, 0, 8

Write the complex number in rectangular form. - $8 \left( \cos \frac { \pi } { 6 } + i \sin \frac { \pi } { 6 } \right)$

The rectangular coordinates of a point are given. Express the point in polar coordinates with $r \geq 0 \text { and } 0 ^ { \circ } \leq \theta < 360 ^ { \circ } \text {. }$ - $\left( \frac { 1 } { 3 } , \frac { - \sqrt { 3 } } { 3 } \right)$

Assume a triangle ABC has standard labeling. Determine whether SAA, ASA, SSA, SAS, or SSS is given. Then decide whether the law of sines or the law of cosines should be used to begin solving the triangle. -a, c, and B

Determine the number of triangles ABC possible with the given parts. - $b = 24 , c = 29 , B = 46 ^ { \circ }$

Find the missing parts of the triangle. - =106. =298 =1353 If necessary, round angles the nearest tenth and side lengths to the nearest $\mathrm { cm }$ .

Find an equivalent equation in rectangular coordinates. - $r = \frac { 2 } { 4 \sin \theta + 6 \cos \theta }$

Write the complex number in rectangular form. - $6 \left( \cos 330 ^ { \circ } + i \sin 330 ^ { \circ } \right)$

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

Two forces act at a point in the plane. The angle between the two forces is given. Find the magnitude of the resultant force. -forces of 40 and 86 newtons, forming an angle of $90 ^ { \circ }$ (round to the nearest newton)

Find the indicated vector. -Let $\mathbf { u } = 3 \mathbf { i } , \mathbf { v } = \mathbf { i } + \mathbf { j }$ . Find $6 \mathbf { u } + \mathbf { v }$

Find all solutions of the equation. Leave answers in trigonometric form. - $x ^ { 3 } + 8 i = 0$

Determine whether the pair of vectors is orthogonal. -3i - 6j, -6i + 3j

Determine the number of triangles ABC possible with the given parts. - $\mathrm { a } = 24 , \mathrm {~b} = 19 , \mathrm {~A} = 43 ^ { \circ }$

Two forces act at a point in the plane. The angle between the two forces is given. Find the magnitude of the resultant force. -forces of $63.6$ and $45.0 \mathrm { lb }$ , forming an angle of $98.5 ^ { \circ }$ (round to the nearest pound)

Solve the problem. -A projectile is fired with an initial velocity of 450 feet per second at an angle of 70° with the horizontal. In how many seconds will the projectile reach its maximum altitude? (Round your Answer to the nearest tenth of a second.)

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 missing parts of the triangle. - =118. a=1263 b=1363 If necessary, round angles to the nearest tenth and side lengths to the nearest cm\mathrm { cm }cm .

Give the rectangular coordinates for the point. - (3,−π3)\left( 3 , - \frac { \pi } { 3 } \right)(3,−3π​)