Preface 

xi  


1  (72) 

Fundamentals for Trigonometry 


2  (2) 







Circular Functions: The Cosine and Sine Functions 


4  (12) 

Special Arcs on the Unit Circle 





Positive and Negative Values of cos t and sin t 





Functional Values for Common Arcs 


16  (11) 

Circular Functional Values for t = 0, π/2, π, 3π/2 



Circular Functional Values for t = π/4 



Circular Functional Values for t = π/6 



Circular Functional Values for t = π/3 





Using a Calculator to Find Functional Values 





Reference Arcs and Functional Values for cos x and sin x, x ER 


27  (13) 



Least Positive Coterminal Arc 



Integer Multiples of Common Arcs 



Functional Values for Arcs with Common Reference Arcs 



Functional Values for Arcs without Common Reference Arcs 



Four Additional Circular Functions: Tangent, Secant, Cosecant, and Cotangent Functions 


40  (13) 



Definitions of the Reciprocal Functions 



Negative Identities and Periods for the Circular Functions 


53  (20) 

Periodic Property of the Circular Functions 



Period of cos x and sin x 



Period of sec x and csc x 



Period of tan x and cot x 



Application of Circular Functions 






63  (3) 


66  (5) 


71  (2) 

Graphs of the Circular Functions 


73  (86) 

Graphs of the Sine and Cosine Functions 


74  (18) 

Graph of the Sine Function 



Graph of the Cosine Function 



Important Characteristics of the Graphs of y = sin x and y = cos x 



Period, Phase Shift, and Other Translations 


92  (17) 

Period Change (Horizontal Shrink or Stretch) 



Combining Period and Amplitude Changes 





Combining Translations with Period and Amplitude Changes 



Finding Equations of Sinusoidal Graphs 



Applications and Modeling with Sinusoidal Functions 


109  (10) 



Models Involving Sinusoidal Functions 



Graphs of the Tangent, Cotangent, Secant, and Cosecant Functions 


119  (14) 

Graph of the Tangent Function 



Graph of the Cotangent Function 



Important Characteristics of the Graphs of y = tan x and y = cot x 



Graphs of the Secant and Cosecant Functions 



Inverses of the Circular Functions 


133  (26) 



Inverse Cosine and Inverse Tangent 



Using a Calculator for Inverse Functional Values 




147  (4) 


151  (4) 


155  (4) 

The Trigonometric Functions 


159  (76) 


160  (13) 









Special Angles Degree and Radian Measure 







Trigonometric and Circular Functions 


173  (12) 

Functional Values for Common Angles 



Solving Right Triangles and Applications 


185  (19) 





Applications of Right Triangles 



Angles of Depression or Elevation 





Solution of Triangles Using Law of Sines 


204  (14) 



Ambiguous Case SSA of the Law of Sines 



Solving the Ambiguous Case 



Application of the Law of Sines 





Solution of Triangles Using Law of Cosines 


218  (17) 



Using the Law of Cosines to Solve the Ambiguous Case (Optional) 






227  (3) 


230  (3) 


233  (2) 


235  (56) 


236  (12) 







Sum and Difference Identities for Cosine 


248  (10) 

Cosine Difference Identity 





Using Cosine Sum or Difference Identities to Find Exact Functional Values 



Sum and Difference Identities for Sine and Tangent 


258  (8) 

Sine Sum and Difference Identities 



Tangent Sum and Difference Identities 



Using Sine and Tangent Sum or Difference Identities to Find Exact Functional Values 




266  (7) 

DoubleAngle Identities for Sine and Cosine 



Using DoubleAngle Identities to Find Exact Functional Values 



Using DoubleAngle Identities to Rewrite Expressions 



HalfAngle and Additional Identities 


273  (18) 

HalfAngle Identities (Formulas) 



Using HalfAngle Identities to Find Exact Functional Values 



Using HalfAngle Identities to Prove Identities and Simplify Expressions 



ProducttoSum and SumtoProduct Identities 




284  (2) 


286  (3) 


289  (2) 


291  (36) 

Solving Conditional Equations I 


292  (6) 

Solving Trigonometric Conditional Equations II 


298  (6) 

More Trigonometric Equations, MultipleAngle Equations 


304  (9) 

Solving Trigonometric Equations Using Identities and Other Strategies 





Using Technology to Solve Trigonometric Equations 






313  (14) 

Graphing Parametric Equations 



Application of Parametric Equations 



Using Technology to Graph Parametric Equations 



Finding Parametric Equations 




322  (1) 


323  (2) 


325  (2) 

Vectors, Polar Equations, and Complex Numbers 


327  (66) 

Geometric Vectors and Applications 


328  (11) 

Vectors Viewed Geometrically 








339  (11) 

Standard Position and Component Form of a Vector 



Magnitude, Direction and Horizontal and Vertical Components 









Finding the Angle Between Two Vectors 



Application of Dot Product 






350  (14) 



Relationship Between Polar Coordinates and Rectangular Coordinates 



Polar Equations and Graphs 




364  (8) 

Standard Form of a Complex Number 



Operations with Complex Numbers 





Geometric Representation of a Complex Number 



Trigonometric Form for Complex Numbers 


372  (21) 



Powers and Roots of Complex Numbers in Trigonometric Form 



Solving Algebraic Equations Using Trigonometry 




385  (4) 


389  (2) 


391  (2) 
Cumulative Review 

393  (6) 
Appendix A Algebra Review 

399  (26) 
Appendix B Geometry Review 

425  
Answers to Selected Exercises 

1  (1) 
Index 

1  