,SOLUTION MANUAL Trigonometry A Unit Circle
Approach, 12th edition Sullivan
Notes
1- The file is chapter after chapter.
2- We have shown you few pages sample.
3- The file contains all Appendix and Excel sheet
if it exists.
4- We have all what you need, we make update
at every time. There are many new editions
waiting you.
5- If you think you purchased the wrong file You
can contact us at every time, we can replace it
with true one.
Our email:
, INSTRUCTOR’S
SOLUTIONS MANUAL
TIM BRITT
Jackson State Community College
TRIGONOMETRY :
A UNIT CIRCLE APPROACH
TWELFTH EDITION
Michael Sullivan
Chicago State University
,Copyright © 2025, 2021, 2017 by Pearson Education, Inc. or its affiliates. All Rights Reserved. Manufactured in the
United States of America. This publication is protected by copyright, and permission should be obtained from the
publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any
means, electronic, mechanical, photocopying, recording, or otherwise. For information regarding permissions, request
forms, and the appropriate contacts within the Pearson Education Global Rights and Permissions department, please
visit www.pearsoned.com/permissions/.
PEARSON and MYLAB are exclusive trademarks owned by Pearson Education, Inc. or its affiliates in the U.S.
and/or other countries.
Unless otherwise indicated herein, any third-party trademarks, logos, or icons that may appear in this work are the
property of their respective owners, and any references to third-party trademarks, logos, icons, or other trade dress are
for demonstrative or descriptive purposes only. Such references are not intended to imply any sponsorship,
endorsement, authorization, or promotion of Pearson’s products by the owners of such marks, or any relationship
between the owner and Pearson Education, Inc., or its affiliates, authors, licensees, or distributors.
PPID: A103000347144
, Table of Contents
Chapter 1 Preliminaries
1.1 The Distance and Midpoint Formulas ......................................................................................... 1
1.2 Graphs of Equations in Two Variables; Intercepts; Symmetry ................................................ 13
1.3 Lines ......................................................................................................................................... 26
1.4 Circles ....................................................................................................................................... 44
Chapter Review................................................................................................................................ 57
Chapter Test ..................................................................................................................................... 63
Chapter Projects ............................................................................................................................... 64
Chapter 2 Functions and Their Graphs
2.1 Functions................................................................................................................................... 65
2.2 The Graph of a Function ........................................................................................................... 83
2.3 Properties of Functions ............................................................................................................. 92
2.4 Library of Functions; Piecewise-defined Functions ............................................................... 109
2.5 Graphing Techniques: Transformations ................................................................................. 121
2.6 Mathematical Models: Building Functions ............................................................................. 139
2.7 One-to-One Functions; Inverse Functions .............................................................................. 146
Chapter Review.............................................................................................................................. 169
Chapter Test ................................................................................................................................... 177
Cumulative Review ....................................................................................................................... 181
Chapter Projects ............................................................................................................................. 184
Chapter 3 Trigonometric Functions
3.1 Angles, Arc Length, and Circular Motion .............................................................................. 186
3.2 Trigonometric Functions: Unit Circle Approach .................................................................... 195
3.3 Properties of the Trigonometric Functions ............................................................................. 213
3.4 Graphs of the Sine and Cosine Functions ............................................................................... 227
3.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions...................................... 248
3.6 Phase Shift; Sinusoidal Curve Fitting ..................................................................................... 258
Chapter Review.............................................................................................................................. 271
Chapter Test ................................................................................................................................... 279
Cumulative Review........................................................................................................................ 282
Chapter Projects ............................................................................................................................. 284
Chapter 4 Analytic Trigonometry
4.1 The Inverse Sine, Cosine, and Tangent Functions .................................................................. 288
4.2 The Inverse Trigonometric Functions (Continued) ................................................................ 302
4.3 Trigonometric Equations ........................................................................................................ 314
4.4 Trigonometric Identities ......................................................................................................... 335
4.5 Sum and Difference Formulas ................................................................................................ 348
4.6 Double-angle and Half-angle Formulas .................................................................................. 373
4.7 Product-to-Sum and Sum-to-Product Formulas...................................................................... 401
Chapter Review.............................................................................................................................. 414
Chapter Test ................................................................................................................................... 429
Cumulative Review........................................................................................................................ 434
Chapter Projects ............................................................................................................................. 438
Copyright © 2025 Pearson Education, Inc.
,Chapter 5 Applications of Trigonometric Functions
5.1 Right Triangle Trigonometry; Applications ........................................................................... 442
5.2 The Law of Sines .................................................................................................................... 456
5.3 The Law of Cosines ................................................................................................................ 470
5.4 Area of a Triangle ................................................................................................................... 483
5.5 Simple Harmonic Motion; Damped Motion; Combining Waves ........................................... 492
Chapter Review.............................................................................................................................. 502
Chapter Test ................................................................................................................................... 509
Cumulative Review........................................................................................................................ 512
Chapter Projects ............................................................................................................................. 516
Chapter 6 Polar Coordinates; Vectors
6.1 Polar Coordinates.................................................................................................................... 520
6.2 Polar Equations and Graphs .................................................................................................... 529
6.3 The Complex Plane; De Moivre’s Theorem ........................................................................... 558
6.4 Vectors .................................................................................................................................... 572
6.5 The Dot Product ...................................................................................................................... 585
6.6 Vectors in Space ..................................................................................................................... 591
6.7 The Cross Product................................................................................................................... 598
Chapter Review.............................................................................................................................. 608
Chapter Test ................................................................................................................................... 618
Cumulative Review........................................................................................................................ 621
Chapter Projects ............................................................................................................................. 623
Chapter 7 Analytic Geometry
7.2 The Parabola ........................................................................................................................... 627
7.3 The Ellipse .............................................................................................................................. 643
7.4 The Hyperbola ........................................................................................................................ 660
7.5 Rotation of Axes; General Form of a Conic ........................................................................... 680
7.6 Polar Equations of Conics ....................................................................................................... 693
7.7 Plane Curves and Parametric Equations ................................................................................. 702
Chapter Review.............................................................................................................................. 716
Chapter Test ................................................................................................................................... 726
Cumulative Review........................................................................................................................ 730
Chapter Projects ............................................................................................................................. 732
Chapter 8 Exponential and Logarithmic Functions
8.1 Exponential Functions ............................................................................................................ 736
8.2 Logarithmic Functions ............................................................................................................ 756
8.3 Properties of Logarithms ........................................................................................................ 778
8.4 Logarithmic and Exponential Equations ................................................................................. 787
8.5 Financial Models .................................................................................................................... 807
8.6 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth
and Decay Models .................................................................................................................... 815
8.7 Building Exponential, Logarithmic, and Logistic Models from Data..................................... 825
Chapter Review.............................................................................................................................. 829
Chapter Test ................................................................................................................................... 838
Chapter Projects ............................................................................................................................. 841
Copyright © 2025 Pearson Education, Inc.
,Appendix A Review
A.1 Algebra Essentials .................................................................................................................. 844
A.2 Geometry Essentials ............................................................................................................... 849
A.3 Polynomials............................................................................................................................ 855
A.4 Solving Equations .................................................................................................................. 863
A.5 Complex Numbers; Quadratic Equations in the Complex Number System .......................... 877
A.6 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications ....... 883
A.7 Interval Notation; Solving Inequalities .................................................................................. 890
A.8 nth Roots; Rational Exponents ................................................................................................ 902
Appendix B Graphing Utilities
B.1 The Viewing Rectangle .......................................................................................................... 912
B.2 Using a Graphing Utility to Graph Equations ........................................................................ 913
B.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry .............................. 918
B.5 Square Screens ....................................................................................................................... 920
Copyright © 2025 Pearson Education, Inc.
,
, Chapter 1
Preliminaries
Section 1.1 (f) Quadrant IV
1. 0
2. 5 3 8 8
3. 32 42 25 5
4. 112 602 121 3600 3721 612
Since the sum of the squares of two of the sides
of the triangle equals the square of the third side,
the triangle is a right triangle.
1 16. (a) Quadrant I
5. bh
2 (b) Quadrant III
(c) Quadrant II
6. true (d) Quadrant I
7. x-coordinate or abscissa; y-coordinate or (e) y-axis
ordinate (f) x-axis
8. quadrants
9. midpoint
10. False; the distance between two points is never
negative.
11. False; points that lie in Quadrant IV will have a
positive x-coordinate and a negative y-coordinate.
The point 1, 4 lies in Quadrant II.
17. The points will be on a vertical line that is two
x x y y2
12. True; M 1 2 , 1 units to the right of the y-axis.
2 2
13. b
14. a
15. (a) Quadrant II
(b) x-axis
(c) Quadrant III
(d) Quadrant I
(e) y-axis
1
Copyright © 2025 Pearson Education, Inc.
, Chapter 1: Preliminaries
18. The points will be on a horizontal line that is
three units above the x-axis. 28. d ( P1 , P2 ) 6 ( 4) 2 2 (3) 2
102 52 100 25
125 5 5
29. d ( P1 , P2 ) 2.3 (0.2) 2 1.1 (0.3) 2
2.52 0.82 6.25 0.64
6.89 2.62
30. d ( P1 , P2 ) 0.3 1.2 2 1.1 2.32
19. d ( P1 , P2 ) (2 0) 2 (1 0) 2 (1.5) 2 (1.2) 2 2.25 1.44
22 12 4 1 5 3.69 1.92
20. d ( P1 , P2 ) (2 0) 2 (1 0) 2 31. d ( P1 , P2 ) (0 a) 2 (0 b) 2
(2) 2 12 4 1 5 ( a ) 2 ( b ) 2 a 2 b 2
21. d ( P1 , P2 ) (2 1) 2 (2 1) 2 32. d ( P1 , P2 ) (0 a ) 2 (0 a) 2
(3) 2 12 9 1 10 (a )2 (a )2
a 2 a 2 2a 2 a 2
22. d ( P1 , P2 ) 2 (1) 2
(2 1) 2
33. A (2,5), B (1,3), C (1, 0)
32 12 9 1 10
d ( A, B ) 1 (2) 2 (3 5)2
23. d ( P1 , P2 ) (5 3) 2 4 4
2
32 (2) 2 9 4 13
22 8 4 64 68 2 17 1 12 (0 3)2
2
d ( B, C )
(2) 2 (3)2 4 9 13
2 1 4 0
2 2
24. d ( P1 , P2 )
d ( A, C ) 1 (2) 2 (0 5)2
3 2
4 9 16 25 5
2
12 (5) 2 1 25 26
25. d ( P1 , P2 ) 4 (7) 2 (0 3)2
112 ( 3) 2 121 9 130
26. d ( P1 , P2 ) 4 2 2 2 (3) 2
22 52 4 25 29
27. d ( P1 , P2 ) (6 5) 2 1 (2)
2
12 32 1 9 10
2
Copyright © 2025 Pearson Education, Inc.
Approach, 12th edition Sullivan
Notes
1- The file is chapter after chapter.
2- We have shown you few pages sample.
3- The file contains all Appendix and Excel sheet
if it exists.
4- We have all what you need, we make update
at every time. There are many new editions
waiting you.
5- If you think you purchased the wrong file You
can contact us at every time, we can replace it
with true one.
Our email:
, INSTRUCTOR’S
SOLUTIONS MANUAL
TIM BRITT
Jackson State Community College
TRIGONOMETRY :
A UNIT CIRCLE APPROACH
TWELFTH EDITION
Michael Sullivan
Chicago State University
,Copyright © 2025, 2021, 2017 by Pearson Education, Inc. or its affiliates. All Rights Reserved. Manufactured in the
United States of America. This publication is protected by copyright, and permission should be obtained from the
publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any
means, electronic, mechanical, photocopying, recording, or otherwise. For information regarding permissions, request
forms, and the appropriate contacts within the Pearson Education Global Rights and Permissions department, please
visit www.pearsoned.com/permissions/.
PEARSON and MYLAB are exclusive trademarks owned by Pearson Education, Inc. or its affiliates in the U.S.
and/or other countries.
Unless otherwise indicated herein, any third-party trademarks, logos, or icons that may appear in this work are the
property of their respective owners, and any references to third-party trademarks, logos, icons, or other trade dress are
for demonstrative or descriptive purposes only. Such references are not intended to imply any sponsorship,
endorsement, authorization, or promotion of Pearson’s products by the owners of such marks, or any relationship
between the owner and Pearson Education, Inc., or its affiliates, authors, licensees, or distributors.
PPID: A103000347144
, Table of Contents
Chapter 1 Preliminaries
1.1 The Distance and Midpoint Formulas ......................................................................................... 1
1.2 Graphs of Equations in Two Variables; Intercepts; Symmetry ................................................ 13
1.3 Lines ......................................................................................................................................... 26
1.4 Circles ....................................................................................................................................... 44
Chapter Review................................................................................................................................ 57
Chapter Test ..................................................................................................................................... 63
Chapter Projects ............................................................................................................................... 64
Chapter 2 Functions and Their Graphs
2.1 Functions................................................................................................................................... 65
2.2 The Graph of a Function ........................................................................................................... 83
2.3 Properties of Functions ............................................................................................................. 92
2.4 Library of Functions; Piecewise-defined Functions ............................................................... 109
2.5 Graphing Techniques: Transformations ................................................................................. 121
2.6 Mathematical Models: Building Functions ............................................................................. 139
2.7 One-to-One Functions; Inverse Functions .............................................................................. 146
Chapter Review.............................................................................................................................. 169
Chapter Test ................................................................................................................................... 177
Cumulative Review ....................................................................................................................... 181
Chapter Projects ............................................................................................................................. 184
Chapter 3 Trigonometric Functions
3.1 Angles, Arc Length, and Circular Motion .............................................................................. 186
3.2 Trigonometric Functions: Unit Circle Approach .................................................................... 195
3.3 Properties of the Trigonometric Functions ............................................................................. 213
3.4 Graphs of the Sine and Cosine Functions ............................................................................... 227
3.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions...................................... 248
3.6 Phase Shift; Sinusoidal Curve Fitting ..................................................................................... 258
Chapter Review.............................................................................................................................. 271
Chapter Test ................................................................................................................................... 279
Cumulative Review........................................................................................................................ 282
Chapter Projects ............................................................................................................................. 284
Chapter 4 Analytic Trigonometry
4.1 The Inverse Sine, Cosine, and Tangent Functions .................................................................. 288
4.2 The Inverse Trigonometric Functions (Continued) ................................................................ 302
4.3 Trigonometric Equations ........................................................................................................ 314
4.4 Trigonometric Identities ......................................................................................................... 335
4.5 Sum and Difference Formulas ................................................................................................ 348
4.6 Double-angle and Half-angle Formulas .................................................................................. 373
4.7 Product-to-Sum and Sum-to-Product Formulas...................................................................... 401
Chapter Review.............................................................................................................................. 414
Chapter Test ................................................................................................................................... 429
Cumulative Review........................................................................................................................ 434
Chapter Projects ............................................................................................................................. 438
Copyright © 2025 Pearson Education, Inc.
,Chapter 5 Applications of Trigonometric Functions
5.1 Right Triangle Trigonometry; Applications ........................................................................... 442
5.2 The Law of Sines .................................................................................................................... 456
5.3 The Law of Cosines ................................................................................................................ 470
5.4 Area of a Triangle ................................................................................................................... 483
5.5 Simple Harmonic Motion; Damped Motion; Combining Waves ........................................... 492
Chapter Review.............................................................................................................................. 502
Chapter Test ................................................................................................................................... 509
Cumulative Review........................................................................................................................ 512
Chapter Projects ............................................................................................................................. 516
Chapter 6 Polar Coordinates; Vectors
6.1 Polar Coordinates.................................................................................................................... 520
6.2 Polar Equations and Graphs .................................................................................................... 529
6.3 The Complex Plane; De Moivre’s Theorem ........................................................................... 558
6.4 Vectors .................................................................................................................................... 572
6.5 The Dot Product ...................................................................................................................... 585
6.6 Vectors in Space ..................................................................................................................... 591
6.7 The Cross Product................................................................................................................... 598
Chapter Review.............................................................................................................................. 608
Chapter Test ................................................................................................................................... 618
Cumulative Review........................................................................................................................ 621
Chapter Projects ............................................................................................................................. 623
Chapter 7 Analytic Geometry
7.2 The Parabola ........................................................................................................................... 627
7.3 The Ellipse .............................................................................................................................. 643
7.4 The Hyperbola ........................................................................................................................ 660
7.5 Rotation of Axes; General Form of a Conic ........................................................................... 680
7.6 Polar Equations of Conics ....................................................................................................... 693
7.7 Plane Curves and Parametric Equations ................................................................................. 702
Chapter Review.............................................................................................................................. 716
Chapter Test ................................................................................................................................... 726
Cumulative Review........................................................................................................................ 730
Chapter Projects ............................................................................................................................. 732
Chapter 8 Exponential and Logarithmic Functions
8.1 Exponential Functions ............................................................................................................ 736
8.2 Logarithmic Functions ............................................................................................................ 756
8.3 Properties of Logarithms ........................................................................................................ 778
8.4 Logarithmic and Exponential Equations ................................................................................. 787
8.5 Financial Models .................................................................................................................... 807
8.6 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth
and Decay Models .................................................................................................................... 815
8.7 Building Exponential, Logarithmic, and Logistic Models from Data..................................... 825
Chapter Review.............................................................................................................................. 829
Chapter Test ................................................................................................................................... 838
Chapter Projects ............................................................................................................................. 841
Copyright © 2025 Pearson Education, Inc.
,Appendix A Review
A.1 Algebra Essentials .................................................................................................................. 844
A.2 Geometry Essentials ............................................................................................................... 849
A.3 Polynomials............................................................................................................................ 855
A.4 Solving Equations .................................................................................................................. 863
A.5 Complex Numbers; Quadratic Equations in the Complex Number System .......................... 877
A.6 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications ....... 883
A.7 Interval Notation; Solving Inequalities .................................................................................. 890
A.8 nth Roots; Rational Exponents ................................................................................................ 902
Appendix B Graphing Utilities
B.1 The Viewing Rectangle .......................................................................................................... 912
B.2 Using a Graphing Utility to Graph Equations ........................................................................ 913
B.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry .............................. 918
B.5 Square Screens ....................................................................................................................... 920
Copyright © 2025 Pearson Education, Inc.
,
, Chapter 1
Preliminaries
Section 1.1 (f) Quadrant IV
1. 0
2. 5 3 8 8
3. 32 42 25 5
4. 112 602 121 3600 3721 612
Since the sum of the squares of two of the sides
of the triangle equals the square of the third side,
the triangle is a right triangle.
1 16. (a) Quadrant I
5. bh
2 (b) Quadrant III
(c) Quadrant II
6. true (d) Quadrant I
7. x-coordinate or abscissa; y-coordinate or (e) y-axis
ordinate (f) x-axis
8. quadrants
9. midpoint
10. False; the distance between two points is never
negative.
11. False; points that lie in Quadrant IV will have a
positive x-coordinate and a negative y-coordinate.
The point 1, 4 lies in Quadrant II.
17. The points will be on a vertical line that is two
x x y y2
12. True; M 1 2 , 1 units to the right of the y-axis.
2 2
13. b
14. a
15. (a) Quadrant II
(b) x-axis
(c) Quadrant III
(d) Quadrant I
(e) y-axis
1
Copyright © 2025 Pearson Education, Inc.
, Chapter 1: Preliminaries
18. The points will be on a horizontal line that is
three units above the x-axis. 28. d ( P1 , P2 ) 6 ( 4) 2 2 (3) 2
102 52 100 25
125 5 5
29. d ( P1 , P2 ) 2.3 (0.2) 2 1.1 (0.3) 2
2.52 0.82 6.25 0.64
6.89 2.62
30. d ( P1 , P2 ) 0.3 1.2 2 1.1 2.32
19. d ( P1 , P2 ) (2 0) 2 (1 0) 2 (1.5) 2 (1.2) 2 2.25 1.44
22 12 4 1 5 3.69 1.92
20. d ( P1 , P2 ) (2 0) 2 (1 0) 2 31. d ( P1 , P2 ) (0 a) 2 (0 b) 2
(2) 2 12 4 1 5 ( a ) 2 ( b ) 2 a 2 b 2
21. d ( P1 , P2 ) (2 1) 2 (2 1) 2 32. d ( P1 , P2 ) (0 a ) 2 (0 a) 2
(3) 2 12 9 1 10 (a )2 (a )2
a 2 a 2 2a 2 a 2
22. d ( P1 , P2 ) 2 (1) 2
(2 1) 2
33. A (2,5), B (1,3), C (1, 0)
32 12 9 1 10
d ( A, B ) 1 (2) 2 (3 5)2
23. d ( P1 , P2 ) (5 3) 2 4 4
2
32 (2) 2 9 4 13
22 8 4 64 68 2 17 1 12 (0 3)2
2
d ( B, C )
(2) 2 (3)2 4 9 13
2 1 4 0
2 2
24. d ( P1 , P2 )
d ( A, C ) 1 (2) 2 (0 5)2
3 2
4 9 16 25 5
2
12 (5) 2 1 25 26
25. d ( P1 , P2 ) 4 (7) 2 (0 3)2
112 ( 3) 2 121 9 130
26. d ( P1 , P2 ) 4 2 2 2 (3) 2
22 52 4 25 29
27. d ( P1 , P2 ) (6 5) 2 1 (2)
2
12 32 1 9 10
2
Copyright © 2025 Pearson Education, Inc.
