Trigonometry

by McKeague, Charles P.

• ISBN13: 9780030247835
• ISBN10: 0030247837
• Format: Hardcover
• Copyright: 1999-07-01
• Publisher: Thomson Learning

Table of Contents

1 The Six Trigonometric Functions	1	(53)
1.1 Angles, Degrees, and Special Triangles	2	(13)
1.2 The Rectangular Coordinate System	15	(14)
1.3 Definition I: Trigonometric Functions	29	(8)
1.4 Introduction to Identities	37	(8)
1.5 More on Identities	45	(5)
Summary	50	(2)
Test	52	(2)
2 Right Triangle Trigonometry	54	(62)
2.1 Definition II: Right Triangle Trigonometry	55	(10)
2.2 Calculators and Trigonometric Functions of an Acute Angle	65	(9)
2.3 Solving Right Triangles	74	(10)
2.4 Applications	84	(14)
2.5 Vectors: A Geometric Approach	98	(12)
Summary	110	(3)
Test	113	(3)
3 Radian Measure	116	(52)
3.1 Reference Angle	117	(8)
3.2 Radians and Degrees	125	(10)
3.3 Definition III: Circular Functions	135	(8)
3.4 Arc Length and Area of a Sector	143	(11)
3.5 Velocities	154	(9)
Summary	163	(3)
Test	166	(2)
4 Graphing and Inverse Functions	168	(78)
4.1 Basic Graphs	169	(14)
4.2 Amplitude and Period	183	(18)
4.3 Phase Shift	201	(13)
4.4 Finding an Equation from Its Graph	214	(12)
4.5 Graphing Combinations of Functions	226	(4)
4.6 Inverse Trigonometric Functions	230	(10)
Summary	240	(3)
Test	243	(3)
5 Identities and Formulas	246	(44)
5.1 Proving Identities	247	(9)
5.2 Sum and Difference Formulas	256	(10)
5.3 Double-Angle Formulas	266	(7)
5.4 Half-Angle Formulas	273	(7)
5.5 Additional Identities	280	(6)
Summary	286	(2)
Test	288	(2)
6 Equations	290	(37)
6.1 Solving Trigonometric Equations	291	(7)
6.2 More on Trigonometric Equations	298	(7)
6.3 Trigonometric Equations Involving Multiple Angles	305	(8)
6.4 Parametric Equations and Further Graphing	313	(11)
Summary	324	(1)
Test	325	(2)
7 Triangles	327	(49)
7.1 The Law of Sines	328	(12)
7.2 The Ambiguous Case	340	(6)
7.3 The Law of Cosines	346	(7)
7.4 The Area of a Triangle	353	(6)
7.5 Vectors: An Algebraic Approach	359	(12)
Summary	371	(3)
Test	374	(2)
8 Complex Numbers and Polar Coordinates	376
8.1 Complex Numbers	377	(8)
8.2 Trigonometric Form for Complex Numbers	385	(5)
8.3 Products and Quotients in Trigonometric Form	390	(6)
8.4 Roots of a Complex Number	396	(7)
8.5 Polar Coordinates	403	(9)
8.6 Equations in Polar Coordinates and Their Graphs	412	(9)
Summary	421	(4)
Test	425
Appendix: Exponential and Logarithmic Functions	A-1
A.1 Exponential Functions	A-2	(9)
A.2 Logarithms Are Exponents	A-11	(7)
A.3 Properties of Logarithms	A-18	(3)
A.4 Common Logarithms and Natural Logarithms	A-21	(7)
A.5 Exponential Equations and Change of Base	A-28	(6)
Answers to Odd-Numbered Exercises and Chapter Tests	A-34
Index	I-1