Trigonometry

by Downing, Douglas A.

• ISBN13: 9780764113604
• ISBN10: 0764113607
• Edition: 3rd
• Format: Paperback
• Copyright: 2001-02-01
• Publisher: Barrons Educational Series Inc

Summary

Here’s a complete, easy-to-grasp course in trigonometry that takes the form of a fantasy novel. The King of Carmorra and his subjects have many practical problems to solve, and their answers can be found by applying principles of trigonometry. Readers follow along and learn to solve many different problems that can be reduced to triangular diagrams. They learn the laws of sine and cosine, trigonometric functions and inverse functions, waves, conic sections, polynomial approximation, and much more. The book is filled with instructive exercises and their solutions, plus illustrative drawings, graphs, and diagrams. This new edition contains updated coverage on using graphing calculators and computer spreadsheets for solving trigonometric problems.

Table of Contents

Introduction	vii
Angles and Triangles	1	(13)
The Rainstorm	1	(1)
Measuring Angles	2	(4)
The Raging River Flood	6	(1)
Triangles to the Rescue	7	(1)
Complete Guide to Triangles	7	(4)
Notes to Chapter 1	11	(1)
Exercises	12	(2)
Solving Right Triangle Problems	14	(13)
The Height of the Tree	14	(5)
Calculating Heights with Similar Triangles	19	(2)
The New Ski Jump	21	(1)
The Shifting Star	22	(1)
The Distance to the Star	23	(2)
Notes to Chapter 2	25	(1)
Exercises	26	(1)
Trigonometric Functions: sin, cos, and tan	27	(19)
Too Many Triangles	27	(1)
The Gremlin's Vile Threat	28	(4)
The Holiday Lighting Display	32	(1)
30--60--90 Triangles	32	(1)
The Decorative Adjustable Triangle	33	(2)
The Sine Ratio	35	(1)
The Tangent Ratio	36	(1)
Functions	36	(1)
Definition of Trigonometric Functions	37	(2)
Notes to Chapter 3	39	(1)
Exercises	40	(6)
Applications of Trigonometric Functions	46	(20)
The Balloon Ride	46	(3)
Velocity Vectors	49	(1)
Component Vectors	49	(2)
The Off-Course River Boat	51	(2)
The Message-Delivering System	53	(2)
The Distance of Travel of the Capsule	55	(1)
The Slippery Slope	56	(2)
Friction	58	(1)
The Maximum Angle of Tilt	59	(1)
The Merry-Go-Round Streamers	60	(1)
Centrifugal Force	60	(2)
Note to Chapter 4	62	(1)
Exercises	63	(3)
Radian Measure	66	(23)
Recordis Writes Out the Table	66	(1)
sin 90°	67	(1)
sin 0°	68	(1)
The Attack of the Killer Bees	69	(1)
Measuring Rotations	70	(1)
Radian Measure	71	(2)
The Special Number π	73	(1)
Converting Radians to Degrees	74	(1)
Coterminal Angles	74	(1)
The Shifting Sun	75	(2)
The Radius of the Earth	77	(1)
Trigonometric Functions	78	(3)
Cofunctions	81	(1)
Cotangent Function	82	(1)
Reciprocal Functions	82	(1)
The Secant and Cosecant Functions	82	(1)
Notes to Chapter 5	83	(2)
Exercises	85	(4)
Trigonometric Identities	89	(12)
Pythagorean Identities	90	(3)
Addition Rules	93	(2)
Double-Angle Rules	95	(1)
Trigonometric Identities	96	(2)
Note to Chapter 6	98	(1)
Exercises	98	(3)
Law of Cosines and Law of Sines	101	(15)
The Triangle with the Unknown Parts	101	(3)
Law of Cosines	104	(2)
Law of Sines	106	(4)
Exercises	110	(6)
Graphs of Trigonometric Functions	116	(19)
The Bouncing Wagon	116	(2)
The Periodic Function	118	(3)
The Graph of the Sine Function	121	(3)
The Graph of the Cosine Function	124	(1)
Graphs of the Tangent and Cotangent Functions	125	(1)
Graphs of the Secant and Cosecant Functions	126	(1)
Alternating Current	127	(1)
Amplitude	127	(2)
Frequency	129	(1)
Phase	130	(1)
Solving an Equation with a Graphing Calculator	131	(2)
Exercises	133	(2)
Waves	135	(14)
The Waves on the Lake	135	(3)
Wavelength	138	(1)
Harmonic Waves	139	(1)
Sound Waves	140	(1)
Adding Sine Functions of Different Frequencies	141	(1)
Standing Waves in Guitar Strings	142	(4)
Music	146	(1)
The Threat of the Terrible Flood	146	(1)
Note to Chapter 9	147	(1)
Exercises	147	(2)
Inverse Trigonometric Functions	149	(12)
Pal's Pet Pigeons to the Rescue	149	(2)
Inverse Functions	151	(1)
The Arctan, Arcsin, and Arccos Functions	151	(4)
Principal Values	155	(1)
Graphs of Inverse Trigonometric Functions	156	(2)
Exercises	158	(3)
Polar Coordinates	161	(13)
The Pigeon Messenger Service	161	(1)
Rectangular Coordinates	162	(1)
Polar Coordinates	163	(3)
Equations in Polar Coordinates	166	(6)
Exercises	172	(2)
Complex Numbers	174	(13)
The Imaginary Number i	174	(1)
Properties of Complex Numbers	175	(1)
Polar Coordinate Form of Complex Numbers	176	(2)
Multiplying Complex Numbers	178	(2)
Powers of Complex Numbers	180	(1)
Roots of Complex Numbers	181	(2)
Notes to Chapter 12	183	(1)
Exercises	184	(3)
Coordinate Rotation and Conic Sections	187	(26)
The Peaceful Bay Town-Planning Problem	187	(3)
Rotated Coordinate Systems	190	(1)
The New Improved Pigeon-Aiming System	190	(1)
Rotations in Polar Coordinates	191	(1)
Rotations in Rectangular Coordinates	192	(2)
The Two-Unknown Quadratic Equation	194	(1)
Circles	195	(1)
Ellipses	195	(2)
Parabolas	197	(1)
Hyperbolas	197	(1)
Conic Sections	198	(2)
Translation of Axes	200	(1)
The Pesky xy Term	201	(1)
The Perplexing Parabola with the Tilted Axis	202	(2)
The Rotated Equation	204	(1)
The Solution of a Second-Degree Two-Unknown Equation	205	(1)
The Graph of the Tilted Ellipse	206	(1)
The Discriminant	207	(2)
Three-Dimensional Rotations and Virtual Reality	209	(1)
Note to Chapter 13	210	(1)
Exercises	210	(3)
Spherical Trigonometry	213	(44)
Mysterious Triangles and riddles	213	(6)
Great Circles and Small Circles	219	(1)
Latitude and Longitude	220	(4)
Spherical Triangles	224	(3)
Spherical Right Triangles	227	(5)
Sailing Along the Shortest Course	232	(1)
Law of Sines and Law of Cosines	233	(4)
The Altitude of the Sun at the Beach	237	(2)
The Celestial Sphere	239	(4)
The Lost Assistant at the Unknown Latitude	243	(3)
Solving Spherical Triangles	246	(2)
Notes to Chapter 14	248	(3)
Exercises	251	(6)
Polynomial Approximation for sin x and cos x	257	(5)
The Quest for the Elusive Algebraic Expression	257	(1)
The Infinite-Degree Polynomial	258	(2)
The Factorial Function	260	(1)
Series Representation of sin x and cos x	260	(1)
Exercises	261	(1)
Answers to Exercises	262	(45)
Glossary	307	(3)
Appendix	310	(14)
Significant Digits	310	(2)
Computer Spreadsheets	312	(8)
Summary of Trigonometric Formulas	320	(4)
Index	324