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Trigonometry For Dummies, 2nd Edition

Book Description

A plain-English guide to the basics of trig

Trigonometry deals with the relationship between the sides and angles of triangles... mostly right triangles. In practical use, trigonometry is a friend to astronomers who use triangulation to measure the distance between stars. Trig also has applications in fields as broad as financial analysis, music theory, biology, medical imaging, cryptology, game development, and seismology.

From sines and cosines to logarithms, conic sections, and polynomials, this friendly guide takes the torture out of trigonometry, explaining basic concepts in plain English and offering lots of easy-to-grasp example problems. It also explains the "why" of trigonometry, using real-world examples that illustrate the value of trigonometry in a variety of careers.

  • Tracks to a typical Trigonometry course at the high school or college level

  • Packed with example trig problems

  • From the author of Trigonometry Workbook For Dummies

  • Trigonometry For Dummies is for any student who needs an introduction to, or better understanding of, high-school to college-level trigonometry.

    Table of Contents

      1. Introduction
        1. About This Book
        2. Foolish Assumptions
        3. Icons Used in This Book
        4. Beyond the Book
        5. Where to Go from Here
      2. Part I: Getting Started with Trigonometry
        1. Chapter 1: Trouncing Trig Technicalities
          1. Taking Trig for a Ride: What Trig Is
            1. Sizing up the basic figures
            2. Angling for position
            3. Triangulating your position
            4. Circling the wagons
          2. Understanding Trig Speak
            1. Defining trig functions
            2. Taming the radicals
          3. Equating and Identifying
          4. Graphing for Gold
            1. Describing graphing scales
            2. Recognizing basic graphs
        2. Chapter 2: Coordinating Your Efforts with Cartesian Coordinates
          1. Starting Out Simple: Plotting Points
            1. Axes, axes, we all fall down
            2. Determining the origin of it all
            3. Plotting x versus y
            4. Cutting the graph into four parts
          2. From Here to There: Calculating Distances
            1. Counting on vertical and horizontal distances
            2. Another slant: Diagonal distances
            3. Using exact values or estimating distances
          3. Getting to the Center of It All
            1. Finding the midpoint of a line segment
            2. Locating the center of a circle
            3. Partitioning line segments further
            4. Pinpointing the center of a triangle
          4. Racing Down the Slope
            1. Slaloming slope formula
            2. Recognizing parallel and perpendicular lines
          5. Defining Circles with Numbers
            1. Centering circles at the origin
            2. Wandering centers
        3. Chapter 3: Functioning Well
          1. Relations versus Functions
            1. Function junction, what's your function?
            2. Using function notation
            3. Determining domain and range
          2. In-Verse Functions: Rhyme or Reason?
            1. Which functions have inverses?
            2. Finding an inverse function
          3. Transforming Functions
            1. Translating a function
            2. Reflecting like a mirror
        4. Chapter 4: Getting Your Degree
          1. Angles, Angles Everywhere: Measuring in Degrees
            1. Slicing a coordinate plane
            2. Looking elsewhere for degree measures
          2. Graphing Angles in Standard Position
            1. Positioning initial and terminal sides
            2. Measuring by quadrants
          3. What's Your Angle? Labeling in Various Ways
            1. Using negative angle measures
            2. Comingling with coterminal angles
            3. Renaming angles: So many aliases
        5. Chapter 5: Dishing Out the Pi: Radians
          1. What's in a Radian?
            1. Relating to a circle
            2. Converting degrees and radians
            3. Highlighting favorites
          2. Making a Clone of Arc
            1. Taking chunks out of circles
            2. Sweeping hands
            3. Going out and about
        6. Chapter 6: Getting It Right with Triangles
          1. Sizing Up Right Triangles
            1. What's so right about them?
            2. The anatomy of a right triangle
          2. Pythagoras Schmythagoras: Demystifying the Pythagorean Theorem
            1. Hitting a Pythagorean triple
            2. Solving for a missing length
          3. In a League of Their Own: Special Right Triangles
            1. 30-60-90 right triangles
            2. Isosceles right triangles
      3. Part II: Trigonometric Functions
        1. Chapter 7: Doing Right by Trig Functions
          1. SohCahToa to the Rescue: How Trig Functions Work
            1. The name game: A right triangle's three sides
            2. The six ratios: Relating the three sides
            3. The sine function: Opposite over hypotenuse
            4. The cosine function: Adjacent over hypotenuse
            5. The tangent function: Opposite over adjacent
            6. All together, now: Using one function to solve for another
            7. Similar right triangles within a right triangle
            8. Socking the rules away: The legend of SohCahToa
          2. Taking It a Step Further: Reciprocal Functions
            1. The cosecant function: Sine flipped upside down
            2. The secant function: Cosine on its head
            3. The cotangent function: Tangent, tails side up
          3. Angling In on Your Favorites
            1. Identifying the most popular angles
            2. Determining the exact values of functions
        2. Chapter 8: Trading Triangles for Circles: Circular Functions
          1. Getting Acquainted with the Unit Circle
            1. Placing points on the unit circle
            2. Finding a missing coordinate
            3. Sticking to rational coordinates
          2. Going Full Circle with the Angles
            1. Staying positive
            2. Being negative or multiplying your angles
            3. Locating and computing reference angles
        3. Chapter 9: Defining Trig Functions Globally
          1. Defining Trig Functions for All Angles
            1. Putting reference angles to use
            2. Labeling the optimists and pessimists
            3. Combining all the rules
          2. Using Coordinates of Circles to Solve for Trig Functions
            1. Calculating with coordinates on the unit circle
            2. Calculating with coordinates on any circle at the origin
          3. Defining Domains and Ranges of Trig Functions
            1. Friendly functions: Sine and cosine
            2. Close cousins of their reciprocals: Cosecant and secant
            3. Brothers out on their own: Tangent and cotangent
        4. Chapter 10: Applying Yourself to Trig Functions
          1. First Things First: Elevating and Depressing
          2. Measuring Tall Buildings with a Single Bound
            1. Rescuing a damsel from a tower
            2. Determining the height of a tree
            3. Measuring the distance between buildings
          3. Measuring Slope
          4. The Sky's (Not) the Limit
            1. Spotting a balloon
            2. Tracking a rocket
            3. Measuring the view of satellite cameras
          5. Calculating Odd Shapes and Maneuvering Corners
            1. Finding the area of a triangular piece of land
            2. Using Heron's Formula
            3. Moving an object around a corner
      4. Part III: Identities
        1. Chapter 11: Identifying Basic Identities
          1. Flipping Functions on Their Backs: Reciprocal Identities
          2. Function to Function: Ratio Identities
          3. Opposites Attract: Opposite-Angle Identities
          4. Revisiting the Classic Theorem: Pythagorean Identities
            1. The mother of all Pythagorean identities
            2. Extending to tangent and secant
            3. Finishing up with cotangent and cosecant
            4. Rearranging the Pythagorean identities
          5. Combining the Identities
            1. The many faces of sine
            2. Working out the versions
        2. Chapter 12: Operating on Identities
          1. Summing It Up
          2. Overcoming the Differences
          3. Doubling Your Money
            1. One plus one equals two sines
            2. Three's a crowd
          4. Halving Fun Yet?
            1. Explaining the ±
            2. Half a tangent is double the fun
            3. Using half-angle identities
        3. Chapter 13: Proving Identities: The Basics
          1. Lining Up the Players
          2. Picking Sides
          3. Working on Both Sides
          4. Going Back to Square One
            1. Changing to sines and cosines
            2. Factoring
            3. Using a little bit of both
        4. Chapter 14: Sleuthing Out Identity Solutions
          1. Fracturing Fractions
            1. Breaking up is hard to do
            2. Finding a common denominator
          2. Using Tricks of the Trig Trade
            1. Multiplying by a conjugate
            2. Squaring both sides
          3. Identifying With the Operations
            1. Adding it up
            2. What difference does it make?
            3. Multiplying your fun
            4. Halving fun, wish you were here
      5. Part IV: Equations and Applications
        1. Chapter 15: Investigating Inverse Trig Functions
          1. Writing It Right
            1. Using the notation
            2. Distinguishing between the few and the many
          2. Determining Domain and Range of Inverse Trig Functions
            1. Inverse sine function
            2. Inverse cosine function
            3. Inverse tangent function
            4. Inverse cotangent function
            5. Inverse secant function
            6. Inverse cosecant function
            7. Summarizing domain and range
        2. Chapter 16: Making Inverse Trig Work for You
          1. Working with Inverses
          2. Getting Friendly with Your Calculator
            1. Changing the mode
            2. Interpreting notation on the calculator
          3. Multiplying the Input
          4. Solving Some Mixed Problems
        3. Chapter 17: Solving Trig Equations
          1. Generating Simple Solutions
          2. Factoring In the Solutions
            1. Finding a greatest common factor
            2. Factoring quadratics
            3. Increasing the degrees in factoring
            4. Factoring by grouping
          3. Using the Quadratic Formula
          4. Incorporating Identities
          5. Finding Multiple-Angle Solutions
          6. Squaring Both Sides
          7. Multiplying Through
          8. Solving with a Graphing Calculator
        4. Chapter 18: Obeying the Laws
          1. Describing the Parts of Triangles
            1. Standardizing the parts
            2. Determining a triangle
          2. Following the Law of Sines
          3. Continuing with the Law of Cosines
            1. Defining the law of cosines
            2. Law of cosines for SAS
            3. Law of cosines for SSS
            4. Being ambiguous
          4. Finding the Areas of Triangles
            1. Finding area with base and height
            2. Finding area with three sides
            3. Finding area with SAS
            4. Finding area with ASA
      6. Part V: The Graphs of Trig Functions
        1. Chapter 19: Graphing Sine and Cosine
          1. The ABCs of Graphing
          2. Waving at the Sine
            1. Describing amplitude and period
            2. Formalizing the sine equation
            3. Translating the sine
          3. Graphing Cosine
            1. Comparing cosine to sine
            2. Using properties to graph cosine
          4. Applying the Sines of the Times
            1. Sunning yourself
            2. Averaging temperature
            3. Taking your temperature
            4. Making a goal
            5. Theorizing with biorhythms
        2. Chapter 20: Graphing Tangent and Cotangent
          1. Checking Out Tangent
            1. Determining the period
            2. Assigning the asymptotes
            3. Fiddling with the tangent
          2. Confronting the Cotangent
        3. Chapter 21: Graphing Other Trig Functions
          1. Seeing the Cosecant for What It Is
            1. Identifying the asymptotes
            2. Using the sine graph
            3. Varying the cosecant
          2. Unveiling the Secant
            1. Determining the asymptotes
            2. Sketching the graph of secant
            3. Fooling around with secant
          3. Laying Out the Inverse Functions
            1. Graphing inverse sine and cosine
            2. Taking on inverse tangent and cotangent
            3. Crafting inverse secant and cosecant
        4. Chapter 22: Topping Off Trig Graphs
          1. The Basics of Trig Equations
          2. Flipping over a horizontal line
            1. Interpreting the equation
          3. Graphing with the General Form
          4. Adding and Subtracting Functions
          5. Applying Yourself to the Task
            1. Measuring the tide
            2. Tracking the deer population
            3. Measuring the movement of an object on a spring
      7. Part VI: The Part of Tens
        1. Chapter 23: Ten Basic Identities . . . Plus Some Bonuses
          1. Reciprocal Identities
          2. Ratio Identities
          3. Pythagorean Identities
          4. Opposite-Angle Identities
          5. Multiple-Angle Identities
        2. Chapter 24: Ten Not-So-Basic Identities
          1. Product-to-Sum Identities
          2. Sum-to-Product Identities
          3. Reduction Formula
          4. Mollweide's Equations
      8. Appendix: Trig Functions Table
      9. About the Author
      10. Cheat Sheet
      11. More Dummies Products