Question 1

Determine two pairs of polar coordinates for the point with 0° ≤ θ < 360°.
-$( - 4 \sqrt { 3 } , 4 \sqrt { 3 } )$

Accepted Answer

A)  $\left( 4 \sqrt { 6 } , 150 ^ { \circ } \right) , \left( - 4 \sqrt { 6 } , 210 ^ { \circ } \right)$ 
B)  $\left( 4 \sqrt { 6 } , 30 ^ { \circ } \right) , \left( - 4 \sqrt { 6 } , 330 ^ { \circ } \right)$ 
C)  $\left( 4 \sqrt { 6 } , 120 ^ { \circ } \right) , \left( - 4 \sqrt { 6 } , 240 ^ { \circ } \right)$ 
D)  $\left( 4 \sqrt { 6 } , 135 ^ { \circ } \right) , \left( - 4 \sqrt { 6 } , 315 ^ { \circ } \right)$ 
A)  $\left( 4 \sqrt { 6 } , 150 ^ { \circ } \right) , \left( - 4 \sqrt { 6 } , 210 ^ { \circ } \right)$ 
B)  $\left( 4 \sqrt { 6 } , 30 ^ { \circ } \right) , \left( - 4 \sqrt { 6 } , 330 ^ { \circ } \right)$ 
C)  $\left( 4 \sqrt { 6 } , 120 ^ { \circ } \right) , \left( - 4 \sqrt { 6 } , 240 ^ { \circ } \right)$ 
D)  $\left( 4 \sqrt { 6 } , 135 ^ { \circ } \right) , \left( - 4 \sqrt { 6 } , 315 ^ { \circ } \right)$

Question 2

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 about the sun, estimate the closest approach of a planet for which $\mathrm { a } = 39$ and $\mathrm { e } = 0.78$ to the sun.

Accepted Answer

A)  9 astronomical units 
B)  15 astronomical units 
C)  4 astronomical units 
D)  69 astronomical units 
A)  9 astronomical units 
B)  15 astronomical units 
C)  4 astronomical units 
D)  69 astronomical units

Question 3

Determine two pairs of polar coordinates for the point with 0° ≤ θ < 360°.
-$( - 4,0 )$

Accepted Answer

A)  $\left( 4,180 ^ { \circ } \right) , \left( - 4,0 ^ { \circ } \right)$ 
B)  $\left( 4,0 ^ { \circ } \right) , \left( - 4,180 ^ { \circ } \right)$ 
C)  $\left( 4,270 ^ { \circ } \right) , \left( - 4,90 ^ { \circ } \right)$ 
D)  $\left( 4,90 ^ { \circ } \right) , \left( - 4,270 ^ { \circ } \right)$ 
A)  $\left( 4,180 ^ { \circ } \right) , \left( - 4,0 ^ { \circ } \right)$ 
B)  $\left( 4,0 ^ { \circ } \right) , \left( - 4,180 ^ { \circ } \right)$ 
C)  $\left( 4,270 ^ { \circ } \right) , \left( - 4,90 ^ { \circ } \right)$ 
D)  $\left( 4,90 ^ { \circ } \right) , \left( - 4,270 ^ { \circ } \right)$

Question 4

Graph the polar equation for θ in [0°, 360°).
-$$r = 4 ( 1 - \sin \theta )$$

Accepted Answer

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

Question 5

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

Accepted Answer

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

Question 6

Write the word or phrase that best completes each statement or answers the question.
-A projectile is launched from the ground with an initial velocity of $\mathrm { v } _ { 0 }$ feet per second at an angle of $\theta ^ { \circ }$ above the horizontal. Write parametric equations in terms of $v _ { 0 }$ and $\theta$ that model the flight of the projectile. Explain how you would use these equations, for given values of $v _ { 0 }$ and $\theta$, to determine the horizontal distance traveled by the projectile.

Accepted Answer

@#LAT-DLM&
First, solve @#LAT-DLM& for @#LAT-DLM& to determi

Question 7

Find all cube roots of the complex number. Leave answers in trigonometric form.
-$4 - 4 i \sqrt { 3 }$

Accepted Answer

A)  $\sqrt [ 3 ] { 4 } \operatorname { cis } 80 ^ { \circ } , \sqrt [ 3 ] { 4 } \operatorname { cis } 200 ^ { \circ } , \sqrt [ 3 ] { 4 } \operatorname { cis } 320 ^ { \circ }$ 
B)  $\sqrt { 8 } \operatorname { cis } 100 ^ { \circ } , \sqrt { 8 } \operatorname { cis } 220 ^ { \circ } , \sqrt { 8 } \operatorname { cis } 340 ^ { \circ }$ 
C)  $\sqrt [ 3 ] { 8 } \operatorname { cis } 100 ^ { \circ } , \sqrt [ 3 ] { 8 } \operatorname { cis } 220 ^ { \circ } , \sqrt [ 3 ] { 8 } \operatorname { cis } 340 ^ { \circ }$ 
D)  $\sqrt { 4 } \operatorname { cis } 60 ^ { \circ } , \sqrt { 4 } \operatorname { cis } 180 ^ { \circ } , \sqrt { 4 } \operatorname { cis } 300 ^ { \circ }$ 
A)  $\sqrt [ 3 ] { 4 } \operatorname { cis } 80 ^ { \circ } , \sqrt [ 3 ] { 4 } \operatorname { cis } 200 ^ { \circ } , \sqrt [ 3 ] { 4 } \operatorname { cis } 320 ^ { \circ }$ 
B)  $\sqrt { 8 } \operatorname { cis } 100 ^ { \circ } , \sqrt { 8 } \operatorname { cis } 220 ^ { \circ } , \sqrt { 8 } \operatorname { cis } 340 ^ { \circ }$ 
C)  $\sqrt [ 3 ] { 8 } \operatorname { cis } 100 ^ { \circ } , \sqrt [ 3 ] { 8 } \operatorname { cis } 220 ^ { \circ } , \sqrt [ 3 ] { 8 } \operatorname { cis } 340 ^ { \circ }$ 
D)  $\sqrt { 4 } \operatorname { cis } 60 ^ { \circ } , \sqrt { 4 } \operatorname { cis } 180 ^ { \circ } , \sqrt { 4 } \operatorname { cis } 300 ^ { \circ }$

Question 8

Solve.
-A complex number $\mathrm { z }$ does not belong to the Mandelbrot set if any of the complex numbers in the sequence $z , z ^ { 2 } + z , \left( z ^ { 2 } + z \right) ^ { 2 } + z , \left[ \left( z ^ { 2 } + z \right) ^ { 2 } + z \right] ^ { 2 } + z , \ldots$ has modulus exceeding 2 . Does $z = 0.1 + 0.4 i$ belong to the Mandelbrot set?

Accepted Answer

A)  Yes 
B)  $\mathrm { No }$ 
A)  Yes 
B)  $\mathrm { No }$

Question 9

Use a table of values to graph the plane curve defined by the following parametric equations. Find a rectangular
equation for the curve.
-$$x = 3 \sin t , y = 3 \cos t \text {, for } t \text { in } [ 0,2 \pi ]$$

Accepted Answer

A) 
 
$x ^ { 2 } + y ^ { 2 } = 9$, for $x$ in $[ - 3,3 ]$ 
B) 
 
$y = \sqrt { a ^ { 2 } - x ^ { 2 } } = 9$, for $x$ in $[ - 3,3 ]$ 
C) 
 
$y = x ^ { 2 } - 9$, for $x$ in $[ - 2,2 ]$ 
D) 
 
$y ^ { 2 } - x ^ { 2 } = 9$, for $x$ in $[ - 3,3 ]$ 
A) 
 
$x ^ { 2 } + y ^ { 2 } = 9$, for $x$ in $[ - 3,3 ]$ 
B) 
 
$y = \sqrt { a ^ { 2 } - x ^ { 2 } } = 9$, for $x$ in $[ - 3,3 ]$ 
C) 
 
$y = x ^ { 2 } - 9$, for $x$ in $[ - 2,2 ]$ 
D) 
 
$y ^ { 2 } - x ^ { 2 } = 9$, for $x$ in $[ - 3,3 ]$

Question 10

Solve the problem.
-An airplane is sighted at the same time by two ground observers who are 5 miles apart and both directly west of the airplane. They report the angles of elevation as $11 ^ { \circ }$ and $24 ^ { \circ }$. How high is the airplane? Round to the nearest hundredth of a mile.

Accepted Answer

A)  $0.95 \mathrm { mi }$ 
B)  $1.73 \mathrm { mi }$ 
C)  $3.68 \mathrm { mi }$ 
D)  $2.03 \mathrm { mi }$ 
A)  $0.95 \mathrm { mi }$ 
B)  $1.73 \mathrm { mi }$ 
C)  $3.68 \mathrm { mi }$ 
D)  $2.03 \mathrm { mi }$

Question 11

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

Accepted Answer

A)  $\langle - 0.98,0.17 \rangle$ 
B)  $\langle - 8.86,1.56 \rangle$ 
C)  $\langle - 8.46,3.08 \rangle$ 
D)  $\langle - 9,1.58 \rangle$ 
A)  $\langle - 0.98,0.17 \rangle$ 
B)  $\langle - 8.86,1.56 \rangle$ 
C)  $\langle - 8.46,3.08 \rangle$ 
D)  $\langle - 9,1.58 \rangle$

Question 12

Find the indicated vector.
-Let $\mathbf { a } = \langle 8,9 \rangle$. Find $9 \mathbf { a }$.

Accepted Answer

A)  $\langle - 72,81 \rangle$ 
B)  $\langle 72 , - 81 \rangle$ 
C)  $\langle - 72 , - 81 \rangle$ 
D)  $\langle 72,81 \rangle$ 
A)  $\langle - 72,81 \rangle$ 
B)  $\langle 72 , - 81 \rangle$ 
C)  $\langle - 72 , - 81 \rangle$ 
D)  $\langle 72,81 \rangle$

Question 13

Determine the number of triangles ABC possible with the given parts.
-$$a = 35 , b = 46 , A = 24 ^ { \circ }$$

Accepted Answer

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

Question 14

Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as
-$$
\begin{array}{l}
a=6.6 \text { in. } \
b=13.1 \text { in. } \
c=16.3 \text { in. }
\end{array}
$$

Accepted Answer

A)  $ \mathrm{A}=22.8^{\circ}, \mathrm{B}=50.2^{\circ}, \mathrm{C}=107^{\circ} $ 
B)  $ \mathrm{A}=20.8^{\circ}, \mathrm{B}=50.2^{\circ}, \mathrm{C}=109^{\circ} $ 
C)  $ A=24.8^{\circ}, B=48.2^{\circ}, C=107^{\circ} $ 
D)  No triangle satisfies the given conditions. 
A)  $ \mathrm{A}=22.8^{\circ}, \mathrm{B}=50.2^{\circ}, \mathrm{C}=107^{\circ} $ 
B)  $ \mathrm{A}=20.8^{\circ}, \mathrm{B}=50.2^{\circ}, \mathrm{C}=109^{\circ} $ 
C)  $ A=24.8^{\circ}, B=48.2^{\circ}, C=107^{\circ} $ 
D)  No triangle satisfies the given conditions.

Question 15

Find the dot product for the pair of vectors.
-$- 5 \mathbf { i } + 7 \mathbf { j } , 13 \mathbf { i } - 6 \mathbf { j }$

Accepted Answer

A)  $- 42$ 
B)  $- 107$ 
C)  $- 23$ 
D)  $- 65$ 
A)  $- 42$ 
B)  $- 107$ 
C)  $- 23$ 
D)  $- 65$

Question 16

Find a rectangular equation for the plane curve defined by the parametric equations.
-$x = 5 \tan t , y = 4 \cot t$

Accepted Answer

A)  $y = \frac { x } { 20 }$ 
B)  $y = \frac { 4 } { 5 } \sin x$ 
C)  $y = \frac { 20 } { x }$ 
D)  $y = \frac { 5 } { 4 } \cos x$ 
A)  $y = \frac { x } { 20 }$ 
B)  $y = \frac { 4 } { 5 } \sin x$ 
C)  $y = \frac { 20 } { x }$ 
D)  $y = \frac { 5 } { 4 } \cos x$

Question 17

Find the dot product for the pair of vectors.
-$7 \mathbf { i } - 2 \mathbf { j } , 8 \mathbf { i } + \mathbf { j }$

Accepted Answer

A)  58 
B)  $- 9$ 
C)  0 
D)  54 
A)  58 
B)  $- 9$ 
C)  0 
D)  54

Question 18

Find the given power. Write answer in rectangular form.
-$( 1 - \mathrm { i } ) ^ { 10 }$

Accepted Answer

A)  32 
B)  $32 - 32 \mathrm { i }$ 
C)  $- 32 \mathrm { i }$ 
D)  $- 32 + 32 \mathrm { i }$ 
A)  32 
B)  $32 - 32 \mathrm { i }$ 
C)  $- 32 \mathrm { i }$ 
D)  $- 32 + 32 \mathrm { i }$

Question 19

Find the component form of the indicated vector.
-Let $\mathbf { u } = \langle 5 , - 1 \rangle , \mathbf { v } = \langle - 7,7 \rangle$. Find $3 u - 5 v$.

Accepted Answer

A)  $\langle - 20,32 \rangle$ 
B)  $\langle 12,0 \rangle$ 
C)  $\langle - 6 , - 30 \rangle$ 
D)  $\langle 50 , - 38 \rangle$ 
A)  $\langle - 20,32 \rangle$ 
B)  $\langle 12,0 \rangle$ 
C)  $\langle - 6 , - 30 \rangle$ 
D)  $\langle 50 , - 38 \rangle$

Question 20

Use the figure to find the specified vector.
-Find $\mathbf { a } + \mathbf { b }$

Accepted Answer

A)  $\langle - 5,3 \rangle$ 
B)  $\langle 11,11 \rangle$ 
C)  $\langle 5,11 \rangle$ 
D)  $\langle - 5,11 \rangle$ 
A)  $\langle - 5,3 \rangle$ 
B)  $\langle 11,11 \rangle$ 
C)  $\langle 5,11 \rangle$ 
D)  $\langle - 5,11 \rangle$

Determine two pairs of polar coordinates for the point with 0° ≤ θ < 360°. - $( - 4 \sqrt { 3 } , 4 \sqrt { 3 } )$

Determine two pairs of polar coordinates for the point with 0° ≤ θ < 360°. - $( - 4,0 )$

Graph the polar equation for θ in [0°, 360°). - $r = 4 ( 1 - \sin \theta )$ $Graph the polar equation for θ in [0°, 360°). - r = 4 ( 1 - \sin \theta )$

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

Find all cube roots of the complex number. Leave answers in trigonometric form. - $4 - 4 i \sqrt { 3 }$

Solve the problem. -An airplane is sighted at the same time by two ground observers who are 5 miles apart and both directly west of the airplane. They report the angles of elevation as $11 ^ { \circ }$ and $24 ^ { \circ }$ . How high is the airplane? Round to the nearest hundredth of a mile.

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

Find the indicated vector. -Let $\mathbf { a } = \langle 8,9 \rangle$ . Find $9 \mathbf { a }$ .

Determine the number of triangles ABC possible with the given parts. - $a = 35 , b = 46 , A = 24 ^ { \circ }$

Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as - a=6.6 in. b=13.1 in. c=16.3 in.

Find the dot product for the pair of vectors. - $- 5 \mathbf { i } + 7 \mathbf { j } , 13 \mathbf { i } - 6 \mathbf { j }$

Find a rectangular equation for the plane curve defined by the parametric equations. - $x = 5 \tan t , y = 4 \cot t$

Find the dot product for the pair of vectors. - $7 \mathbf { i } - 2 \mathbf { j } , 8 \mathbf { i } + \mathbf { j }$

Find the given power. Write answer in rectangular form. - $( 1 - \mathrm { i } ) ^ { 10 }$

Find the component form of the indicated vector. -Let $\mathbf { u } = \langle 5 , - 1 \rangle , \mathbf { v } = \langle - 7,7 \rangle$ . Find $3 u - 5 v$ .

Use the figure to find the specified vector. -Find $\mathbf { a } + \mathbf { b }$ $Use the figure to find the specified vector. -Find \mathbf { a } + \mathbf { b }$

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

Filters

Exam 8: Applications of Trigonometry

Determine two pairs of polar coordinates for the point with 0° ≤ θ < 360°. - (−43,43)( - 4 \sqrt { 3 } , 4 \sqrt { 3 } )(−43​,43​)

Determine two pairs of polar coordinates for the point with 0° ≤ θ < 360°. - (−4,0)( - 4,0 )(−4,0)

Graph the polar equation for θ in [0°, 360°). - r=4(1−sin⁡θ)r = 4 ( 1 - \sin \theta )r=4(1−sinθ)

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

Find all cube roots of the complex number. Leave answers in trigonometric form. - 4−4i34 - 4 i \sqrt { 3 }4−4i3​

Use a table of values to graph the plane curve defined by the following parametric equations. Find a rectangular equation for the curve. - x=3sin⁡t,y=3cos⁡t, for t in [0,2π]x = 3 \sin t , y = 3 \cos t \text {, for } t \text { in } [ 0,2 \pi ]x=3sint,y=3cost, for t in [0,2π]

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

Find the indicated vector. -Let a=⟨8,9⟩\mathbf { a } = \langle 8,9 \ranglea=⟨8,9⟩ . Find 9a9 \mathbf { a }9a .

Determine the number of triangles ABC possible with the given parts. - a=35,b=46,A=24∘a = 35 , b = 46 , A = 24 ^ { \circ }a=35,b=46,A=24∘

Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as - a=6.6 in. b=13.1 in. c=16.3 in.

Find the dot product for the pair of vectors. - −5i+7j,13i−6j- 5 \mathbf { i } + 7 \mathbf { j } , 13 \mathbf { i } - 6 \mathbf { j }−5i+7j,13i−6j

Find a rectangular equation for the plane curve defined by the parametric equations. - x=5tan⁡t,y=4cot⁡tx = 5 \tan t , y = 4 \cot tx=5tant,y=4cott

Find the dot product for the pair of vectors. - 7i−2j,8i+j7 \mathbf { i } - 2 \mathbf { j } , 8 \mathbf { i } + \mathbf { j }7i−2j,8i+j

Find the given power. Write answer in rectangular form. - (1−i)10( 1 - \mathrm { i } ) ^ { 10 }(1−i)10

Find the component form of the indicated vector. -Let u=⟨5,−1⟩,v=⟨−7,7⟩\mathbf { u } = \langle 5 , - 1 \rangle , \mathbf { v } = \langle - 7,7 \rangleu=⟨5,−1⟩,v=⟨−7,7⟩ . Find 3u−5v3 u - 5 v3u−5v .

Use the figure to find the specified vector. -Find a+b\mathbf { a } + \mathbf { b }a+b

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

Filters

Determine two pairs of polar coordinates for the point with 0° ≤ θ < 360°. - $( - 4 \sqrt { 3 } , 4 \sqrt { 3 } )$

Determine two pairs of polar coordinates for the point with 0° ≤ θ < 360°. - $( - 4,0 )$

Graph the polar equation for θ in [0°, 360°). - $r = 4 ( 1 - \sin \theta )$ $Graph the polar equation for θ in [0°, 360°). - r = 4 ( 1 - \sin \theta )$

Find all cube roots of the complex number. Leave answers in trigonometric form. - $4 - 4 i \sqrt { 3 }$

Find the indicated vector. -Let $\mathbf { a } = \langle 8,9 \rangle$ . Find $9 \mathbf { a }$ .

Determine the number of triangles ABC possible with the given parts. - $a = 35 , b = 46 , A = 24 ^ { \circ }$

Find the dot product for the pair of vectors. - $- 5 \mathbf { i } + 7 \mathbf { j } , 13 \mathbf { i } - 6 \mathbf { j }$

Find a rectangular equation for the plane curve defined by the parametric equations. - $x = 5 \tan t , y = 4 \cot t$

Find the dot product for the pair of vectors. - $7 \mathbf { i } - 2 \mathbf { j } , 8 \mathbf { i } + \mathbf { j }$

Find the given power. Write answer in rectangular form. - $( 1 - \mathrm { i } ) ^ { 10 }$

Find the component form of the indicated vector. -Let $\mathbf { u } = \langle 5 , - 1 \rangle , \mathbf { v } = \langle - 7,7 \rangle$ . Find $3 u - 5 v$ .

Use the figure to find the specified vector. -Find $\mathbf { a } + \mathbf { b }$ $Use the figure to find the specified vector. -Find \mathbf { a } + \mathbf { b }$