Trigonometry and Its Applications,9780070290747

Trigonometry and Its Applications

by
ISBN13: 9780070290747
ISBN10: 0070290741
Format: Hardcover
Pub. Date: 1990-06-01
Publisher(s): Glencoe/McGraw-Hill School Pub
List Price: $59.96

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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

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