Question 1

Find sum of the pair of complex numbers.
--9i, -4i

Accepted Answer

A)  -13i 
B)  -9 - 4i 
C)  -4 - 9i 
D)  -13 
A)  -13i 
B)  -9 - 4i 
C)  -4 - 9i 
D)  -13

Question 2

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

Accepted Answer

A)  $\langle 6.73,25.11 \rangle$ 
B)  $\langle 0.26,0.97 \rangle$ 
C)  $\langle 10.99,23.56 \rangle$ 
D)  $\langle 25.11,6.73 \rangle$ 
A)  $\langle 6.73,25.11 \rangle$ 
B)  $\langle 0.26,0.97 \rangle$ 
C)  $\langle 10.99,23.56 \rangle$ 
D)  $\langle 25.11,6.73 \rangle$

Question 3

Perform the indicated operation. Give answers in rectangular form expressing real and imaginary parts to four decimal
places.
-$\left[ 28.6 \operatorname { cis } \frac { 2 \pi } { 7 } \right] ^ { 2 }$

Accepted Answer

A)  $797.4520 - 182.0132 \mathrm { i }$ 
B)  $- 182.0132 + 797.4520 \mathrm { i }$ 
C)  $509.9897 + 639.5069 \mathrm { i }$ 
D)  $- 6.3641 + 27.8829 \mathrm { i }$ 
A)  $797.4520 - 182.0132 \mathrm { i }$ 
B)  $- 182.0132 + 797.4520 \mathrm { i }$ 
C)  $509.9897 + 639.5069 \mathrm { i }$ 
D)  $- 6.3641 + 27.8829 \mathrm { i }$

Question 4

Find the missing parts of the triangle.
- 
If necessary, round angles to the nearest degree and give exact values of side lengths.

Accepted Answer

A)  $\mathrm { B } = 90 ^ { \circ } , \mathrm { C } = 60 ^ { \circ } , \mathrm { b } = 8 \sqrt { 3 }$ 
B)  $B = 60 ^ { \circ } , C = 90 ^ { \circ } , b = 8$ 
C)  no such triangle 
D)  $B = 60 ^ { \circ } , C = 90 ^ { \circ } , b = 8 \sqrt { 3 }$ 
A)  $\mathrm { B } = 90 ^ { \circ } , \mathrm { C } = 60 ^ { \circ } , \mathrm { b } = 8 \sqrt { 3 }$ 
B)  $B = 60 ^ { \circ } , C = 90 ^ { \circ } , b = 8$ 
C)  no such triangle 
D)  $B = 60 ^ { \circ } , C = 90 ^ { \circ } , b = 8 \sqrt { 3 }$

Question 5

Find sum of the pair of complex numbers.
-8 + 8i, 5i

Accepted Answer

A)  8 + 3i 
B)  8 - 40i 
C)  8 + 13i 
D)  8 + 40i 
A)  8 + 3i 
B)  8 - 40i 
C)  8 + 13i 
D)  8 + 40i

Question 6

Find the component form of the indicated vector.
-Let $\mathbf { u } = \langle - 5 , - 2 \rangle$. Find $- 7 \mathbf { u }$.

Accepted Answer

A)  $\langle 35,14 \rangle$ 
B)  $\langle - 35,14 \rangle$ 
C)  $\langle - 35 , - 14 \rangle$ 
D)  $\langle 35 , - 14 \rangle$ 
A)  $\langle 35,14 \rangle$ 
B)  $\langle - 35,14 \rangle$ 
C)  $\langle - 35 , - 14 \rangle$ 
D)  $\langle 35 , - 14 \rangle$

Question 7

Find an equivalent equation in rectangular coordinates.
-$$r = \cos \theta$$

Accepted Answer

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

Question 8

Find all solutions of the equation. Leave answers in trigonometric form.
-$$x ^ { 5 } - 243 = 0$$

Accepted Answer

A)  $\{ 3 , - 3 \}$ 
B)  $\left\{ 3 \operatorname { cis } \frac { \pi } { 5 } , 3 \operatorname { cis } \frac { 3 \pi } { 5 } , 3 \operatorname { cis } \pi , 3 \operatorname { cis } \frac { 7 \pi } { 5 } , 3 \operatorname { cis } \frac { 9 \pi } { 5 } \right\}$ 
C)  $\left\{ 243 \operatorname { cis } 0,243 \operatorname { cis } \frac { 2 \pi } { 5 } , 243 \operatorname { cis } \frac { 4 \pi } { 5 } , 243 \operatorname { cis } \frac { 6 \pi } { 5 } , 243 \operatorname { cis } \frac { 8 \pi } { 5 } \right\}$ 
D)  $\left\{ 3 \operatorname { cis } 0,3 \operatorname { cis } \frac { 2 \pi } { 5 } , 3 \operatorname { cis } \frac { 4 \pi } { 5 } , 3 \operatorname { cis } \frac { 6 \pi } { 5 } , 3 \operatorname { cis } \frac { 8 \pi } { 5 } \right\}$ 
A)  $\{ 3 , - 3 \}$ 
B)  $\left\{ 3 \operatorname { cis } \frac { \pi } { 5 } , 3 \operatorname { cis } \frac { 3 \pi } { 5 } , 3 \operatorname { cis } \pi , 3 \operatorname { cis } \frac { 7 \pi } { 5 } , 3 \operatorname { cis } \frac { 9 \pi } { 5 } \right\}$ 
C)  $\left\{ 243 \operatorname { cis } 0,243 \operatorname { cis } \frac { 2 \pi } { 5 } , 243 \operatorname { cis } \frac { 4 \pi } { 5 } , 243 \operatorname { cis } \frac { 6 \pi } { 5 } , 243 \operatorname { cis } \frac { 8 \pi } { 5 } \right\}$ 
D)  $\left\{ 3 \operatorname { cis } 0,3 \operatorname { cis } \frac { 2 \pi } { 5 } , 3 \operatorname { cis } \frac { 4 \pi } { 5 } , 3 \operatorname { cis } \frac { 6 \pi } { 5 } , 3 \operatorname { cis } \frac { 8 \pi } { 5 } \right\}$

Question 9

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.
-$$\begin{array} { l } 
\mathrm { A } = 21.3 ^ { \circ } \
\mathrm { b } = 12.2 \mathrm { in } . \
\mathrm { c } = 5.3 \mathrm { in }
\end{array}$$

Accepted Answer

A)  $32.1$ in. 2 
B)  $9.7$ in.2 
C)  $30.1$ in. 2 
D)  $11.7$ in. 2 
A)  $32.1$ in. 2 
B)  $9.7$ in.2 
C)  $30.1$ in. 2 
D)  $11.7$ in. 2

Question 10

The rectangular coordinates of a point are given. Express the point in polar coordinates with $$r \geq 0 \text { and } 0 ^ { \circ } \leq \theta < 360 ^ { \circ } \text {. }$$
-$$\left( \frac { 1 } { 5 } , \frac { \sqrt { 3 } } { 5 } \right)$$

Accepted Answer

A)  $\left( \frac { 2 } { 5 } , 30 ^ { \circ } \right)$ 
B)  $\left( \frac { 1 } { 5 } , 30 ^ { \circ } \right)$ 
C)  $\left( \frac { 2 } { 5 } , 60 ^ { \circ } \right)$ 
D)  $\left( \frac { 2 } { 5 } , 120 ^ { \circ } \right)$ 
A)  $\left( \frac { 2 } { 5 } , 30 ^ { \circ } \right)$ 
B)  $\left( \frac { 1 } { 5 } , 30 ^ { \circ } \right)$ 
C)  $\left( \frac { 2 } { 5 } , 60 ^ { \circ } \right)$ 
D)  $\left( \frac { 2 } { 5 } , 120 ^ { \circ } \right)$

Question 11

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

Accepted Answer

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

Question 12

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as
an angle in $$\left[ 0,360 ^ { \circ } \right]$$
-$\langle - 5 \sqrt { 3 } , 5 \rangle$

Accepted Answer

A)  $10 ; 330 ^ { \circ }$ 
B)  $20 ; 30 ^ { \circ }$ 
C)  $20 ; 150 ^ { \circ }$ 
D)  $10 ; 150 ^ { \circ }$ 
A)  $10 ; 330 ^ { \circ }$ 
B)  $20 ; 30 ^ { \circ }$ 
C)  $20 ; 150 ^ { \circ }$ 
D)  $10 ; 150 ^ { \circ }$

Question 13

Determine whether the pair of vectors is orthogonal.
-3i - 8j, -8i - 3j

Accepted Answer

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

Question 14

Use a table of values to graph the plane curve defined by the following parametric equations. Find a rectangular equation
for the curve.
-$x = 8 \sin t , y = 8 \cos t$, for $t$ in $[ 0,2 \pi ]$

Accepted Answer

A) 
 
$y = x ^ { 2 } - 9$, for $x$ in $[ - 2,2 ]$ 
B) 
 
$y = \sqrt { a ^ { 2 } - x ^ { 2 } } = 64$, for $x$ in $[ - 8,8 ]$ 
C) 
 
$x ^ { 2 } + y ^ { 2 } = 64$, for $x$ in $[ - 8,8 ]$ 
D) 
 
$y ^ { 2 } - x ^ { 2 } = 64$, for $x$ in $[ - 8,8 ]$ 
A) 
 
$y = x ^ { 2 } - 9$, for $x$ in $[ - 2,2 ]$ 
B) 
 
$y = \sqrt { a ^ { 2 } - x ^ { 2 } } = 64$, for $x$ in $[ - 8,8 ]$ 
C) 
 
$x ^ { 2 } + y ^ { 2 } = 64$, for $x$ in $[ - 8,8 ]$ 
D) 
 
$y ^ { 2 } - x ^ { 2 } = 64$, for $x$ in $[ - 8,8 ]$

Question 15

Answer the question.
-With respect to what line are the 6 sixth roots of $- 1$ symmetric?

Accepted Answer

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

Question 16

Determine two pairs of polar coordinates for the point with $$0 ^ { \circ } \leq \theta < 360 ^ { \circ }$$
-$( - 15,5 \sqrt { 3 } )$

Accepted Answer

A)  $\left( 10 \sqrt { 3 } , 60 ^ { \circ } \right) , \left( - 10 \sqrt { 3 } , 300 ^ { \circ } \right)$ 
B)  $\left( 10 \sqrt { 3 } , 150 ^ { \circ } \right) , \left( - 10 \sqrt { 3 } , 330 ^ { \circ } \right)$ 
C)  $\left( 10 \sqrt { 3 } , 120 ^ { \circ } \right) , \left( - 15 \sqrt { 3 } , 240 ^ { \circ } \right)$ 
D)  $\left( 10 \sqrt { 3 } , 30 ^ { \circ } \right) , \left( - 10 \sqrt { 3 } , 330 ^ { \circ } \right)$ 
A)  $\left( 10 \sqrt { 3 } , 60 ^ { \circ } \right) , \left( - 10 \sqrt { 3 } , 300 ^ { \circ } \right)$ 
B)  $\left( 10 \sqrt { 3 } , 150 ^ { \circ } \right) , \left( - 10 \sqrt { 3 } , 330 ^ { \circ } \right)$ 
C)  $\left( 10 \sqrt { 3 } , 120 ^ { \circ } \right) , \left( - 15 \sqrt { 3 } , 240 ^ { \circ } \right)$ 
D)  $\left( 10 \sqrt { 3 } , 30 ^ { \circ } \right) , \left( - 10 \sqrt { 3 } , 330 ^ { \circ } \right)$

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 pilot wants to fly on a bearing of $60.9 ^ { \circ }$. By flying due east, he finds that a $57 - \mathrm { mph }$ wind, blowing from the south, puts him on course. Find the ground speed of the plane.

Accepted Answer

A)  $117 \mathrm { mph }$ 
B)  $176 \mathrm { mph }$ 
C)  $65 \mathrm { mph }$ 
D)  $234 \mathrm { mph }$ 
A)  $117 \mathrm { mph }$ 
B)  $176 \mathrm { mph }$ 
C)  $65 \mathrm { mph }$ 
D)  $234 \mathrm { mph }$

Question 18

Solve the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.
-$$\begin{array} { l } 
B = 15.8 ^ { \circ } \
C = 102.9 ^ { \circ } \
b = 33.7
\end{array}$$

Accepted Answer

A)  $\mathrm { A } = 61.3 ^ { \circ } , \mathrm { a } = 108.6 , \mathrm { c } = 120.6$ 
B)  $\mathrm { A } = 59.3 ^ { \circ } , \mathrm { a } = 122.6 , \mathrm { c } = 110.6$ 
C)  $\mathrm { A } = 61.3 ^ { \circ } , \mathrm { a } = 110.6 , \mathrm { c } = 122.6$ 
D)  $\mathrm { A } = 59.3 ^ { \circ } , \mathrm { a } = 120.6 , \mathrm { c } = 108.6$ 
A)  $\mathrm { A } = 61.3 ^ { \circ } , \mathrm { a } = 108.6 , \mathrm { c } = 120.6$ 
B)  $\mathrm { A } = 59.3 ^ { \circ } , \mathrm { a } = 122.6 , \mathrm { c } = 110.6$ 
C)  $\mathrm { A } = 61.3 ^ { \circ } , \mathrm { a } = 110.6 , \mathrm { c } = 122.6$ 
D)  $\mathrm { A } = 59.3 ^ { \circ } , \mathrm { a } = 120.6 , \mathrm { c } = 108.6$

Question 19

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

Accepted Answer

A)  $\langle 0.5 , - 0.87 \rangle$ 
B)  $\langle 56.56 , - 67.41 \rangle$ 
C)  $\langle 44 , - 76.21 \rangle$ 
D)  $\langle 88 , - 152.42 \rangle$ 
A)  $\langle 0.5 , - 0.87 \rangle$ 
B)  $\langle 56.56 , - 67.41 \rangle$ 
C)  $\langle 44 , - 76.21 \rangle$ 
D)  $\langle 88 , - 152.42 \rangle$

Question 20

Graph the polar equation for $$\theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right)$$
-$$r = 8 \sin 2 \theta$$

Accepted Answer

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

Find sum of the pair of complex numbers. --9i, -4i

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

Perform the indicated operation. Give answers in rectangular form expressing real and imaginary parts to four decimal places. - $\left[ 28.6 \operatorname { cis } \frac { 2 \pi } { 7 } \right] ^ { 2 }$

Find the missing parts of the triangle. - If necessary, round angles to the nearest degree and give exact values of side lengths.

Find sum of the pair of complex numbers. -8 + 8i, 5i

Find the component form of the indicated vector. -Let $\mathbf { u } = \langle - 5 , - 2 \rangle$ . Find $- 7 \mathbf { u }$ .

Find an equivalent equation in rectangular coordinates. - $r = \cos \theta$

Find all solutions of the equation. Leave answers in trigonometric form. - $x ^ { 5 } - 243 = 0$

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary. - =21. =12.2. =5.3

The rectangular coordinates of a point are given. Express the point in polar coordinates with $r \geq 0 \text { and } 0 ^ { \circ } \leq \theta < 360 ^ { \circ } \text {. }$ - $\left( \frac { 1 } { 5 } , \frac { \sqrt { 3 } } { 5 } \right)$

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

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in $\left[ 0,360 ^ { \circ } \right]$ - $\langle - 5 \sqrt { 3 } , 5 \rangle$

Determine whether the pair of vectors is orthogonal. -3i - 8j, -8i - 3j

Answer the question. -With respect to what line are the 6 sixth roots of $- 1$ symmetric?

Determine two pairs of polar coordinates for the point with $0 ^ { \circ } \leq \theta < 360 ^ { \circ }$ - $( - 15,5 \sqrt { 3 } )$

Solve the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate. - B=15. C=102. b=33.7

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

Graph the polar equation for $\theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right)$ - $r = 8 \sin 2 \theta$ $Graph the polar equation for \theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right) - r = 8 \sin 2 \theta$

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 sum of the pair of complex numbers. --9i, -4i

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

Perform the indicated operation. Give answers in rectangular form expressing real and imaginary parts to four decimal places. - [28.6cis⁡2π7]2\left[ 28.6 \operatorname { cis } \frac { 2 \pi } { 7 } \right] ^ { 2 }[28.6cis72π​]2

Find the missing parts of the triangle. - If necessary, round angles to the nearest degree and give exact values of side lengths.

Find sum of the pair of complex numbers. -8 + 8i, 5i

Find the component form of the indicated vector. -Let u=⟨−5,−2⟩\mathbf { u } = \langle - 5 , - 2 \rangleu=⟨−5,−2⟩ . Find −7u- 7 \mathbf { u }−7u .

Find an equivalent equation in rectangular coordinates. - r=cos⁡θr = \cos \thetar=cosθ

Find all solutions of the equation. Leave answers in trigonometric form. - x5−243=0x ^ { 5 } - 243 = 0x5−243=0

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary. - =21. =12.2. =5.3

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

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in [0,360∘]\left[ 0,360 ^ { \circ } \right][0,360∘] - ⟨−53,5⟩\langle - 5 \sqrt { 3 } , 5 \rangle⟨−53​,5⟩

Determine whether the pair of vectors is orthogonal. -3i - 8j, -8i - 3j

Use a table of values to graph the plane curve defined by the following parametric equations. Find a rectangular equation for the curve. - x=8sin⁡t,y=8cos⁡tx = 8 \sin t , y = 8 \cos tx=8sint,y=8cost , for ttt in [0,2π][ 0,2 \pi ][0,2π]

Answer the question. -With respect to what line are the 6 sixth roots of −1- 1−1 symmetric?

Determine two pairs of polar coordinates for the point with 0∘≤θ<360∘0 ^ { \circ } \leq \theta < 360 ^ { \circ }0∘≤θ<360∘ - (−15,53)( - 15,5 \sqrt { 3 } )(−15,53​)

Solve the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate. - B=15. C=102. b=33.7

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

Graph the polar equation for θ in [0∘,360∘)\theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right)θ in [0∘,360∘) - r=8sin⁡2θr = 8 \sin 2 \thetar=8sin2θ

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

Perform the indicated operation. Give answers in rectangular form expressing real and imaginary parts to four decimal places. - $\left[ 28.6 \operatorname { cis } \frac { 2 \pi } { 7 } \right] ^ { 2 }$

Find the component form of the indicated vector. -Let $\mathbf { u } = \langle - 5 , - 2 \rangle$ . Find $- 7 \mathbf { u }$ .

Find an equivalent equation in rectangular coordinates. - $r = \cos \theta$

Find all solutions of the equation. Leave answers in trigonometric form. - $x ^ { 5 } - 243 = 0$

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in $\left[ 0,360 ^ { \circ } \right]$ - $\langle - 5 \sqrt { 3 } , 5 \rangle$

Answer the question. -With respect to what line are the 6 sixth roots of $- 1$ symmetric?

Determine two pairs of polar coordinates for the point with $0 ^ { \circ } \leq \theta < 360 ^ { \circ }$ - $( - 15,5 \sqrt { 3 } )$

Graph the polar equation for $\theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right)$ - $r = 8 \sin 2 \theta$ $Graph the polar equation for \theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right) - r = 8 \sin 2 \theta$