Trigonometry and Its Applications

by Schoen, Harold L.

• ISBN13: 9780070290747
• ISBN10: 0070290741
• Format: Hardcover
• Copyright: 1990-06-01
• Publisher: Glencoe/McGraw-Hill School Pub

Table of Contents

Preface	vii
Introduction: Problem Solving, Mathematical Connections, and Technology	ix
Trigonometric Functions	1	(66)
The Coordinate Plane and Angles	1	(7)
Functions	8	(8)
Algebra Review	16	(1)
Sine, Cosine, and Tangent Functions	16	(6)
Cosecant, Secant, and Cotangent Functions	22	(8)
Midchapter Review	27	(2)
Geometry Review	29	(1)
Values of Trigonometric Functions for Special Angles	30	(6)
Evaluating Trigonometric Functions	36	(9)
Extension: Snell's Law	43	(2)
Radian Measure	45	(6)
Applications of Radian Measure	51	(16)
Using BASIC: Computing Values of Trigonometric Functions	57	(2)
Chapter Summary and Review	59	(4)
Chapter Test	63	(4)
Trigonometric Identities	67	(56)
Basic Identities	67	(7)
Algebra Review	73	(1)
Verifying Identities	74	(9)
Using BASIC: Discovering Identities and Counterexamples	80	(3)
Sum and Difference Identities for Cosine	83	(8)
Sum and Difference Identities for Sine	91	(6)
Midchapter Review	96	(1)
Algebra Review	97	(1)
Sum and Difference Identities for Tangent	97	(5)
Double-Angle Identities	102	(7)
Half-Angle Identities	109	(14)
Extension: Product and Sum Identities	114	(3)
Chapter Summary and Review	117	(3)
Chapter Test	120	(3)
Circular Functions And Their Graphs	123	(70)
The Circular Functions	123	(9)
Graphs of Sine and Cosine Functions	132	(8)
Amplitude	140	(5)
Period	145	(10)
Midchapter Review	152	(1)
Algebra Review	153	(1)
Extension: AM/FM Radio Waves	153	(2)
Phase Shift	155	(7)
Graphs of Sums of Sinusoids	162	(4)
Graphs of Tangent and Cotangent Functions	166	(6)
Graphs of Secant and Cosecant Functions	172	(4)
Circular Functions as mathematical Models	176	(17)
Using BASIC: Computer Graphing of Circular Functions	183	(3)
Chapter Summary and Review	186	(4)
Chapter Test	190	(3)
Inverses of Circular and Trigonometric Functions	193	(48)
Inverse of a Function	193	(5)
Inverse Sine and Cosine Functions	198	(6)
Inverse Tangent and Cotangent Functions	204	(7)
Algebra Review	209	(2)
Inverse Secant and Cosecant Functions	211	(4)
Midchapter Review	214	(1)
Trigonometric Equations	215	(7)
Extension: Equations Involving Trigonometric and Algebraic Terms	220	(2)
Polar Coordinates	222	(6)
Graphs of Polar Equations	228	(13)
Using BASIC: Computing Area Under a Curve	233	(2)
Chapter Summary and Review	235	(2)
Chapter Test	237	(4)
Triangles and Trigonomety	241	(62)
Solving Right Triangles	241	(8)
Geometry Review	249	(1)
Law of Cosines	249	(7)
Navigation and Travel Applications	256	(7)
Extension: Approximate Numbers	261	(2)
Law of Sines	263	(8)
Midchapter Review	270	(1)
Surveying Applications	271	(6)
The Side-Side-Angle Case	277	(6)
Area of a Triangle	283	(5)
Further Applications	288	(15)
Using BASIC: Solving Triangles	293	(2)
Chapter Summary and Review	295	(4)
Chapter Test	299	(4)
Vectors and Trigonometry	303	(44)
Introduction to Vectors	303	(9)
Vectors in the Coordinate Plane	312	(7)
Displacement and Velocity Applications	319	(8)
Extension: Wind Velocity Aboard Ship	324	(2)
Midchapter Review	326	(1)
Inner Product of Two Vectors	327	(4)
Force and Work Applications	331	(16)
Using BASIC: Computing Vector Angles and Magnitudes	338	(3)
Chapter Summary and Review	341	(2)
Chapter Test	343	(4)
Complex numbers and Trigonometry	347	(42)
Addition and Subtraction of Complex Numbers	347	(5)
Multiplication and Division of Complex Numbers	352	(7)
Extension: Fields	358	(1)
Graphical Representations of Complex Numbers	359	(5)
Midchapter Review	363	(1)
Trigonometric Form of Complex Numbers	364	(6)
De Moivre's Theorem	370	(5)
Roots of Complex Numbers	375	(14)
Using BASIC: Computing with Complex Numbers	379	(3)
Chapter Summary and Review	382	(4)
Chapter Test	386	(3)
Circular Functions and Series	389	(49)
Sequences	389	(8)
Series	397	(7)
An Intuitive Approach to Limits	404	(11)
Extension: Further Applications of Limits	411	(2)
Midchapter Review	413	(2)
Limits	415	(7)
Using BASIC: Computing Limits	420	(2)
Power Series Representations of Circular Functions	422	(5)
Hyperbolic Functions	427	(11)
Chapter Summary and Review	432	(3)
Chapter Test	435	(3)
Appendix A BASIC Programming	438	(7)
Appendix B Using Graphing Calculators	445	(7)
Appendix C Using Trigonometric Tables	452	(3)
Table of Values of the Trigonometric Functions	455	(9)
Glossary	464	(7)
Selected Answers	471	(54)
Index	525