The Humongous Book of Trigonometry Problems by W. Michael Kelley
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About this book :-
The Humongous Book of Trigonometry Problems written by
W Michael Kelley
Most math and science study guides are a reflection of the college professors who write them-dry, difficult, and pretentious.
The Humongous Book of Trigonometry Problems is the exception. Author Mike Kelley has taken what appears to be a typical trigonometry workbook, chock full of solved problems — more than 750! — and made notes in the margins adding missing steps and simplifying concepts and solutions, so what would be baffling to students is made perfectly clear. No longer will befuddled students wonder where a particular answer came from or have to rely on trial and error to solve problems. And by learning how to interpret and solve problems as they are presented in a standard trigonometry course, students become fully prepared to solve those difficult, obscure problems that were never discussed in class but always seem to find their way onto exams.
Book Detail :-
Title: The Humongous Book of Trigonometry Problems
Edition:
Author(s): W Michael Kelley
Publisher: Alpha
Series:
Year: 2012
Pages: 455
Type: PDF
Language: English
ISBN: 1615641823,9781615641826
Country: US
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About Author :-
Author W. Michael Kelley famous mathematian. He is a former award-winning calculus teacher and the author of six math books, including The Complete Idiot’s Guide to Algebra, Second Edition, and The Humongous Book of Calculus Problems. Kelley received an award from the Maryland Council of Teachers of Mathematics recognizing him as an Outstanding High School Mathematics Teacher and four-years-running title of Most Popular Teacher in his home school. Kelley is also the founder and editor of calculus-help.com.
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Book Contents :-
The Humongous Book of Trigonometry Problems written by
W Michael Kelley
cover the following topics.
Introduction
1. Angles and Arcs [Pairs of rays and pieces of circle]
Standard Position [Angles, front and center]
Measuring Angles [Degrees, radians, rotations]
Converting Between Angle Measurements [Especially degrees and radians]
Complementary and Supplementary Angles [Sums of 90° and 180°]
Arc Length [To measure arcs, you first measure angles]
2. Right Triangle Trigonometry [Including all six trig functions]
Pythagorean Theorem [a2 + b2 = c2]
Trigonometric Functions [sin, cos, tan, cot, sec, and csc]
Trigonometric Tables [When “close enough” is good enough]
Calculator-Generated Trigonometric Values [So long, trig tables]
3. The Unit Circle [A little circle, a lot of memorizing]
45°–45°–90° Triangles [ ]
30°–60°–90° Triangles [ ]
Cosine and Sine in the First Quadrant [As easy as ]
Common Angles on the Unit Circle [And their cosine/sine values]
4. Trigonometric Values of General Angles [Think outside the unit circle]
Reference Angles [Shrink rays that turn any angles into acute angles]
Coterminal Angles [Two angles that end at the same ray]
Angles Beyond the Unit Circle [Calculating trig values you didn’t memorize]
5. Graphing Sine and Cosine Functions [Get on the right wavelength]
Periodic Functions [Graphs that repeat and sort of look like a heartbeat]
Transforming Periodic Graphs [Move, stretch, squish, and flip graphs]
Sine Functions [Oscillating between –1 and 1, until you transform them]
Cosine Functions [The sine graph schooched slightly to the left]
6. Graphing Other Trigonometric Functions [Tan, cot, sec, and csc]
Tangent [Large function values, limited domain]
Cotangent [A reflection of tangent]
Secant [U-shaped pieces that shoot off of the cosine graph]
Cosecant [Similar to secant, but based off of sine]
7. Basic Trigonometric Identities [Simplifyingtrig statements]
Reciprocal and Cofunction Identities [Cos is reciprocal of sec, cofunction of sin]
Negative Identities [What happens when you plug in –x?]
Pythagorean Identities [For example, cos2 x + sin2 x = 1]
Sum and Difference Formulas for Sine and Cosine [Expanding things like sin (x + y)]
8. Advanced Trigonometric Identities [“Advanced” means “brimming with fractions”]
Double-Angle Formulas [Ditch the 2s in sin 2x and cos 2y]
Power-Reducing Formulas [Rewrite squared functions using double angles]
Half-Angle Formulas [Win half an argument by being radical]
Product-to-Sum Identities [Add or subtract, instead of multiplying, trig functions]
Sum-to-Product Identities [Do the opposite of the last section]
Tangent Identities [Sum/difference, double/half-angle, and power-reducing formulas]
9. Inverse Trigonometric Functions [Arccosine, arcsine, arctangent]
Graphs of Inverse Trigonometric Functions [Including domain and range]
General and Exact Solutions [One vs. many answers]
10. Simple Trigonometric Equations [Algebra 1, but with angles]
Linear Equations [Add, subtract, multiply, and divide both sides by the same thing]
Zero Products [Factoring]
Quadratic Formula [When you can’t factor]
Functions of Multiple Angles [Instead of cos x = 1, solve cos 5x = 1]
11. Advanced Trigonometric Equations [Trickier equations = clever-er solutions]
Square Roots [Eliminating squares instead of factoring them]
Rational Equations [Fractions with trigonometric numerators and denominators]
Pythagorean Identities [Convert one trig function into another]
Squaring [With squares come Pythagorean identities]
Applying Trigonometric Identities [Other than the Pythagorean identities]
12. Area of Triangles and Sectors [Three-sided polygons and pieces of pie]
Base and Height [Half of base times height]
Trigonometric Area Formulas [SAS, ASA, and AAS triangle area formulas]
Heron’s Formula [SSS triangle area formula]
Area of a Sector [Surface area of a pizza slice]
13. Oblique Triangle Laws [Oblique = Not a right triangle]
Law of Sines [Given AAS, ASA, and occasionally SSA]
Law of Cosines [Given SAS or SSS]
14. Vectors
Plotting Vectors [Using initial and terminal points]
Component Form [Move the initial point to the origin]
Magnitude [How long is the vector?]
Unit Vectors [Vectors with a magnitude of 1]
15. Basic Vector Operations [Add/subtract vectors and multiply by scalars]
Adding and Subtracting Graphically [Head-to-tail technique]
Adding and Subtracting Algebraically [Calculate + ]
Scalar Multiplication [Calculate c ]
Identifying Components Given Magnitude and Direction [Instead of coordinates]
16. Advanced Vector Operations [All about the dot product]
Dot Product [Looks like multiplication, but it’s not]
Measuring Angles Between Vectors [The dot product in disguise]
Orthogonal Vectors [Perpendicular vectors]
Vector Projections and Work [Create specific orthogonal vectors]
17. Parametric Equations and Polar Coordinates [Different ways to map the coordinate plane]
Parametric Equations [Two equations that describe one curve]
Polar Coordinates [Plot points using distances and angles]
Converting Between Polar and Rectangular Form [Given points or equations]
Polar Graphs [They can be hard to BEAR (get it?)]
18. Trigonometry of Complex Numbers [You can’t spell “trig” without “i”]
Rectangular Form of Complex Numbers [Add, subtract, multiply, divide, and graph]
Trigonometric Form of Complex Numbers [The reason you learned polar coordinates]
Multiplying and Dividing Trigonometric Form [By plugging into one of two formulas]
De Moivre’s Theorem [Raising complex numbers to powers]
Roots of Complex Numbers [Square roots, cube roots, etc.]
Appendix A. Table of Trigonometric Values [Nine pages that answer the question “Why do I need a calculator?”]
Appendix B. The Unit Circle [Just in case you didn’t memorize it]
Appendix C. Formulas and Identities [To memorize or reference]
Index
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