Question 1

Find the angle between the pair of vectors to the nearest tenth of a degree.
--8, 9 , -9, -6

Accepted Answer

A)  41.1° 
B)  82.1° 
C)  31.1° 
D)  92.1° 
A)  41.1° 
B)  82.1° 
C)  31.1° 
D)  92.1° B

Question 2

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

Accepted Answer

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

Question 3

Sketch the vectors u and w with angle $\theta$ between them and sketch the resultant.
-$$| \mathbf { u } | = 5 , | \mathbf { w } | = 5 , \theta = 45 ^ { \circ }$$

Accepted Answer

A) 
  
B) 
  
A) 
  
B) 
  A

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.
-B, a, and c

Accepted Answer

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

Question 5

Sketch the vectors u and w with angle $\theta$ between them and sketch the resultant.
-$$| \mathbf { u } | = 8 , | \mathbf { w } | = 16 , \theta = 15 ^ { \circ }$$

Accepted Answer

A) 
  
B) 
  
A) 
  
B)

Question 6

Find all solutions of the equation. Leave answers in trigonometric form.
-$$x ^ { 2 } - 36 = 0$$

Accepted Answer

A)  $\left\{ 6 \right.$ cis $90 ^ { \circ } , 6$ cis $\left. 270 ^ { \circ } \right\}$ 
B)  $\left\{ 6 \operatorname { cis } 180 ^ { \circ } , 6 \operatorname { cis } 0 ^ { \circ } \right\}$ 
C)  $\left\{ 6 \sqrt { 2 } \operatorname { cis } 45 ^ { \circ } , 6 \sqrt { 2 } \operatorname { cis } 225 ^ { \circ } \right\}$ 
D)  $\left\{ 6 \sqrt { 2 } \operatorname { cis } 235 ^ { \circ } , 6 \sqrt { 2 } \operatorname { cis } 135 ^ { \circ } \right\}$ 
A)  $\left\{ 6 \right.$ cis $90 ^ { \circ } , 6$ cis $\left. 270 ^ { \circ } \right\}$ 
B)  $\left\{ 6 \operatorname { cis } 180 ^ { \circ } , 6 \operatorname { cis } 0 ^ { \circ } \right\}$ 
C)  $\left\{ 6 \sqrt { 2 } \operatorname { cis } 45 ^ { \circ } , 6 \sqrt { 2 } \operatorname { cis } 225 ^ { \circ } \right\}$ 
D)  $\left\{ 6 \sqrt { 2 } \operatorname { cis } 235 ^ { \circ } , 6 \sqrt { 2 } \operatorname { cis } 135 ^ { \circ } \right\}$

Question 7

Find all cube roots of the complex number. Leave answers in trigonometric form.
-$125 \mathrm { i }$

Accepted Answer

A)  5 cis $0 ^ { \circ } , 5 \operatorname { cis } 120 ^ { \circ } , 5$ cis $240 ^ { \circ }$ 
B)  $5 \operatorname { cis } 60 ^ { \circ } , 5 \operatorname { cis } 180 ^ { \circ } , 5 \operatorname { cis } 300 ^ { \circ }$ 
C)  $1 , - 1 , - \mathrm { i }$ 
D)  $5 \operatorname { cis } 30 ^ { \circ } , 5 \operatorname { cis } 150 ^ { \circ } , 5 \operatorname { cis } 270 ^ { \circ }$ 
A)  5 cis $0 ^ { \circ } , 5 \operatorname { cis } 120 ^ { \circ } , 5$ cis $240 ^ { \circ }$ 
B)  $5 \operatorname { cis } 60 ^ { \circ } , 5 \operatorname { cis } 180 ^ { \circ } , 5 \operatorname { cis } 300 ^ { \circ }$ 
C)  $1 , - 1 , - \mathrm { i }$ 
D)  $5 \operatorname { cis } 30 ^ { \circ } , 5 \operatorname { cis } 150 ^ { \circ } , 5 \operatorname { cis } 270 ^ { \circ }$

Question 8

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations.
-$x = - 6 t + 2 , y = 5 t - 8 ; t = - 4$

Accepted Answer

A)  $( - 8 , - 7 )$ 
B)  $( - 4 , - 3 )$ 
C)  $( 22 , - 12 )$ 
D)  $( 26 , - 28 )$ 
A)  $( - 8 , - 7 )$ 
B)  $( - 4 , - 3 )$ 
C)  $( 22 , - 12 )$ 
D)  $( 26 , - 28 )$

Question 9

Determine two pairs of polar coordinates for the point with $$0 ^ { \circ } \leq \theta < 360 ^ { \circ }$$
-$( 4 , - 4 )$

Accepted Answer

A)  $\left( 4 \sqrt { 2 } , 225 ^ { \circ } \right) , \left( - 4 \sqrt { 2 } , 45 ^ { \circ } \right)$ 
B)  $\left( 4 \sqrt { 2 } , 135 ^ { \circ } \right) , \left( - 4 \sqrt { 2 } , 315 ^ { \circ } \right)$ 
C)  $\left( 4 \sqrt { 2 } , 315 ^ { \circ } \right) , \left( - 4 \sqrt { 2 } , 135 ^ { \circ } \right)$ 
D)  $\left( 4 \sqrt { 2 } , 45 ^ { \circ } \right) , \left( - 4 \sqrt { 2 } , 225 ^ { \circ } \right)$ 
A)  $\left( 4 \sqrt { 2 } , 225 ^ { \circ } \right) , \left( - 4 \sqrt { 2 } , 45 ^ { \circ } \right)$ 
B)  $\left( 4 \sqrt { 2 } , 135 ^ { \circ } \right) , \left( - 4 \sqrt { 2 } , 315 ^ { \circ } \right)$ 
C)  $\left( 4 \sqrt { 2 } , 315 ^ { \circ } \right) , \left( - 4 \sqrt { 2 } , 135 ^ { \circ } \right)$ 
D)  $\left( 4 \sqrt { 2 } , 45 ^ { \circ } \right) , \left( - 4 \sqrt { 2 } , 225 ^ { \circ } \right)$

Question 10

Find the dot product for the pair of vectors.
-10, 0, 11, -8

Accepted Answer

A)  102 
B)  118 
C)  -80 
D)  110 
A)  102 
B)  118 
C)  -80 
D)  110

Question 11

Is the given number z in the Julia set?
-z = -0.9i

Accepted Answer

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

Question 12

Graph the cycloid for t in the indicated interval.
-$$x = 7 t - 7 \sin t , y = 7 - 7 \cos t , - 2 \pi \leq t \leq 2 \pi$$

Accepted Answer

A) 
  
B)

C)  
  
D) 
  
A) 
  
B)

C)  
  
D)

Question 13

Is the given number z in the Julia set?
-z = 1 - 0i

Accepted Answer

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

Question 14

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as
an angle in $$\left[ 0,360 ^ { \circ } \right]$$
-$\langle - 12,5 \rangle$

Accepted Answer

A)  $13 ; 112.6 ^ { \circ }$ 
B)  $13 ; 157.4 ^ { \circ }$ 
C)  $15 ; 157.4 ^ { \circ }$ 
D)  $13 ; 22.6 ^ { \circ }$ 
A)  $13 ; 112.6 ^ { \circ }$ 
B)  $13 ; 157.4 ^ { \circ }$ 
C)  $15 ; 157.4 ^ { \circ }$ 
D)  $13 ; 22.6 ^ { \circ }$

Question 15

Graph the polar equation for $$\theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right)$$
-$$r = 5 ( 1 - \sin \theta )$$

Accepted Answer

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

Question 16

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

Accepted Answer

A) 4)7, 1.82 
B) 1)71, 4.7 
C) 4)7, 1.71 
D) 0)94, 0.34 
A) 4)7, 1.82 
B) 1)71, 4.7 
C) 4)7, 1.71 
D) 0)94, 0.34

Question 17

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

Accepted Answer

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

Question 18

Find the polar coordinates of the point(s) of intersection of the given curves for 0 $$0 \leq \theta < 2 \pi$$
-$r = 1 , r = 1 + \sin \theta$

Accepted Answer

A)  $( 1,0 ) , ( 1 , \pi )$ 
B)  $( 0,0 ) , ( 1,0 ) , ( 1 , \pi )$ 
C)  $( 0,0 ) , ( 0,1 ) , ( \pi , 1 )$ 
D)  $( 0,1 ) , ( \pi , 1 )$ 
A)  $( 1,0 ) , ( 1 , \pi )$ 
B)  $( 0,0 ) , ( 1,0 ) , ( 1 , \pi )$ 
C)  $( 0,0 ) , ( 0,1 ) , ( \pi , 1 )$ 
D)  $( 0,1 ) , ( \pi , 1 )$

Question 19

Find all cube roots of the complex number. Leave answers in trigonometric form.
-125

Accepted Answer

A)  $5 \operatorname { cis } 45 ^ { \circ } , 5 \operatorname { cis } 165 ^ { \circ } , 5 \operatorname { cis } 325 ^ { \circ }$ 
B)  $5 \operatorname { cis } 90 ^ { \circ } , 5 \operatorname { cis } 210 ^ { \circ } , 5 \operatorname { cis } 330 ^ { \circ }$ 
C)  $5 \operatorname { cis } 0 ^ { \circ } , 5 \operatorname { cis } 120 ^ { \circ } , 5 \operatorname { cis } 240 ^ { \circ }$ 
D)  $5 \operatorname { cis } 0 ^ { \circ } , 5 \operatorname { cis } 60 ^ { \circ } , 5 \operatorname { cis } 120 ^ { \circ }$ 
A)  $5 \operatorname { cis } 45 ^ { \circ } , 5 \operatorname { cis } 165 ^ { \circ } , 5 \operatorname { cis } 325 ^ { \circ }$ 
B)  $5 \operatorname { cis } 90 ^ { \circ } , 5 \operatorname { cis } 210 ^ { \circ } , 5 \operatorname { cis } 330 ^ { \circ }$ 
C)  $5 \operatorname { cis } 0 ^ { \circ } , 5 \operatorname { cis } 120 ^ { \circ } , 5 \operatorname { cis } 240 ^ { \circ }$ 
D)  $5 \operatorname { cis } 0 ^ { \circ } , 5 \operatorname { cis } 60 ^ { \circ } , 5 \operatorname { cis } 120 ^ { \circ }$

Question 20

Determine two pairs of polar coordinates for the point with $$0 ^ { \circ } \leq \theta < 360 ^ { \circ }$$
-$( - 2 \sqrt { 3 } , 2 \sqrt { 3 } )$

Accepted Answer

A)  $\left( 2 \sqrt { 6 } , 150 ^ { \circ } \right) , \left( - 2 \sqrt { 6 } , 210 ^ { \circ } \right)$ 
B)  $\left( 2 \sqrt { 6 } , 30 ^ { \circ } \right) , \left( - 2 \sqrt { 6 } , 330 ^ { \circ } \right)$ 
C)  $\left( 2 \sqrt { 6 } , 135 ^ { \circ } \right) , \left( - 2 \sqrt { 6 } , 315 ^ { \circ } \right)$ 
D)  $\left( 2 \sqrt { 6 } , 120 ^ { \circ } \right) , \left( - 2 \sqrt { 6 } , 240 ^ { \circ } \right)$ 
A)  $\left( 2 \sqrt { 6 } , 150 ^ { \circ } \right) , \left( - 2 \sqrt { 6 } , 210 ^ { \circ } \right)$ 
B)  $\left( 2 \sqrt { 6 } , 30 ^ { \circ } \right) , \left( - 2 \sqrt { 6 } , 330 ^ { \circ } \right)$ 
C)  $\left( 2 \sqrt { 6 } , 135 ^ { \circ } \right) , \left( - 2 \sqrt { 6 } , 315 ^ { \circ } \right)$ 
D)  $\left( 2 \sqrt { 6 } , 120 ^ { \circ } \right) , \left( - 2 \sqrt { 6 } , 240 ^ { \circ } \right)$

Find the angle between the pair of vectors to the nearest tenth of a degree. --8, 9 , -9, -6

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

Sketch the vectors u and w with angle $\theta$ between them and sketch the resultant. - $| \mathbf { u } | = 5 , | \mathbf { w } | = 5 , \theta = 45 ^ { \circ }$

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

Sketch the vectors u and w with angle $\theta$ between them and sketch the resultant. - $| \mathbf { u } | = 8 , | \mathbf { w } | = 16 , \theta = 15 ^ { \circ }$

Find all solutions of the equation. Leave answers in trigonometric form. - $x ^ { 2 } - 36 = 0$

Find all cube roots of the complex number. Leave answers in trigonometric form. - $125 \mathrm { i }$

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations. - $x = - 6 t + 2 , y = 5 t - 8 ; t = - 4$

Determine two pairs of polar coordinates for the point with $0 ^ { \circ } \leq \theta < 360 ^ { \circ }$ - $( 4 , - 4 )$

Find the dot product for the pair of vectors. -10, 0, 11, -8

Is the given number z in the Julia set? -z = -0.9i

Graph the cycloid for t in the indicated interval. - $x = 7 t - 7 \sin t , y = 7 - 7 \cos t , - 2 \pi \leq t \leq 2 \pi$ $Graph the cycloid for t in the indicated interval. - x = 7 t - 7 \sin t , y = 7 - 7 \cos t , - 2 \pi \leq t \leq 2 \pi$

Is the given number z in the Julia set? -z = 1 - 0i

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in $\left[ 0,360 ^ { \circ } \right]$ - $\langle - 12,5 \rangle$

Graph the polar equation for $\theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right)$ - $r = 5 ( 1 - \sin \theta )$ $Graph the polar equation for \theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right) - r = 5 ( 1 - \sin \theta )$

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

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

Find the polar coordinates of the point(s) of intersection of the given curves for 0 $0 \leq \theta < 2 \pi$ - $r = 1 , r = 1 + \sin \theta$

Find all cube roots of the complex number. Leave answers in trigonometric form. -125

Determine two pairs of polar coordinates for the point with $0 ^ { \circ } \leq \theta < 360 ^ { \circ }$ - $( - 2 \sqrt { 3 } , 2 \sqrt { 3 } )$

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 angle between the pair of vectors to the nearest tenth of a degree. --8, 9 , -9, -6

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

Sketch the vectors u and w with angle θ\thetaθ between them and sketch the resultant. - ∣u∣=5,∣w∣=5,θ=45∘| \mathbf { u } | = 5 , | \mathbf { w } | = 5 , \theta = 45 ^ { \circ }∣u∣=5,∣w∣=5,θ=45∘

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

Sketch the vectors u and w with angle θ\thetaθ between them and sketch the resultant. - ∣u∣=8,∣w∣=16,θ=15∘| \mathbf { u } | = 8 , | \mathbf { w } | = 16 , \theta = 15 ^ { \circ }∣u∣=8,∣w∣=16,θ=15∘

Find all solutions of the equation. Leave answers in trigonometric form. - x2−36=0x ^ { 2 } - 36 = 0x2−36=0

Find all cube roots of the complex number. Leave answers in trigonometric form. - 125i125 \mathrm { i }125i

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations. - x=−6t+2,y=5t−8;t=−4x = - 6 t + 2 , y = 5 t - 8 ; t = - 4x=−6t+2,y=5t−8;t=−4

Determine two pairs of polar coordinates for the point with 0∘≤θ<360∘0 ^ { \circ } \leq \theta < 360 ^ { \circ }0∘≤θ<360∘ - (4,−4)( 4 , - 4 )(4,−4)

Find the dot product for the pair of vectors. -10, 0, 11, -8

Is the given number z in the Julia set? -z = -0.9i

Graph the cycloid for t in the indicated interval. - x=7t−7sin⁡t,y=7−7cos⁡t,−2π≤t≤2πx = 7 t - 7 \sin t , y = 7 - 7 \cos t , - 2 \pi \leq t \leq 2 \pix=7t−7sint,y=7−7cost,−2π≤t≤2π

Is the given number z in the Julia set? -z = 1 - 0i

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∘] - ⟨−12,5⟩\langle - 12,5 \rangle⟨−12,5⟩

Graph the polar equation for θ in [0∘,360∘)\theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right)θ in [0∘,360∘) - r=5(1−sin⁡θ)r = 5 ( 1 - \sin \theta )r=5(1−sinθ)

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

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

Find the polar coordinates of the point(s) of intersection of the given curves for 0 0≤θ<2π0 \leq \theta < 2 \pi0≤θ<2π - r=1,r=1+sin⁡θr = 1 , r = 1 + \sin \thetar=1,r=1+sinθ

Find all cube roots of the complex number. Leave answers in trigonometric form. -125

Determine two pairs of polar coordinates for the point with 0∘≤θ<360∘0 ^ { \circ } \leq \theta < 360 ^ { \circ }0∘≤θ<360∘ - (−23,23)( - 2 \sqrt { 3 } , 2 \sqrt { 3 } )(−23​,23​)

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

Sketch the vectors u and w with angle $\theta$ between them and sketch the resultant. - $| \mathbf { u } | = 5 , | \mathbf { w } | = 5 , \theta = 45 ^ { \circ }$

Sketch the vectors u and w with angle $\theta$ between them and sketch the resultant. - $| \mathbf { u } | = 8 , | \mathbf { w } | = 16 , \theta = 15 ^ { \circ }$

Find all solutions of the equation. Leave answers in trigonometric form. - $x ^ { 2 } - 36 = 0$

Find all cube roots of the complex number. Leave answers in trigonometric form. - $125 \mathrm { i }$

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations. - $x = - 6 t + 2 , y = 5 t - 8 ; t = - 4$

Determine two pairs of polar coordinates for the point with $0 ^ { \circ } \leq \theta < 360 ^ { \circ }$ - $( 4 , - 4 )$

Graph the cycloid for t in the indicated interval. - $x = 7 t - 7 \sin t , y = 7 - 7 \cos t , - 2 \pi \leq t \leq 2 \pi$ $Graph the cycloid for t in the indicated interval. - x = 7 t - 7 \sin t , y = 7 - 7 \cos t , - 2 \pi \leq t \leq 2 \pi$

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in $\left[ 0,360 ^ { \circ } \right]$ - $\langle - 12,5 \rangle$

Graph the polar equation for $\theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right)$ - $r = 5 ( 1 - \sin \theta )$ $Graph the polar equation for \theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right) - r = 5 ( 1 - \sin \theta )$

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

Find the polar coordinates of the point(s) of intersection of the given curves for 0 $0 \leq \theta < 2 \pi$ - $r = 1 , r = 1 + \sin \theta$

Determine two pairs of polar coordinates for the point with $0 ^ { \circ } \leq \theta < 360 ^ { \circ }$ - $( - 2 \sqrt { 3 } , 2 \sqrt { 3 } )$