Trigonometry For Dummies E-Book

Mary Jane Sterling

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch
• Veröffentlichungsjahr: 2014

Seitenzahl: 442

Beschreibung

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.

Leseprobe

Trigonometry For Dummies®, 2nd Edition

Published by: John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, www.wiley.com

Copyright © 2014 by John Wiley & Sons, Inc., Hoboken, New Jersey

Published simultaneously in Canada

No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the Publisher. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, [phone], fax [phone], or online at http://www.wiley.com/go/permissions.

Trademarks: Wiley, For Dummies, the Dummies Man logo, Dummies.com, Making Everything Easier, and related trade dress are trademarks or registered trademarks of John Wiley & Sons, Inc., and may not be used without written permission. All other trademarks are the property of their respective owners. John Wiley & Sons, Inc., is not associated with any product or vendor mentioned in this book.

LIMIT OF LIABILITY/DISCLAIMER OF WARRANTY: WHILE THE PUBLISHER AND AUTHOR HAVE USED THEIR BEST EFFORTS IN PREPARING THIS BOOK, THEY MAKE NO REPRESENTATIONS OR WARRANTIES WITH RESPECT TO THE ACCURACY OR COMPLETENESS OF THE CONTENTS OF THIS BOOK AND SPECIFICALLY DISCLAIM ANY IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. NO WARRANTY MAY BE CREATED OR EXTENDED BY SALES REPRESENTATIVES OR WRITTEN SALES MATERIALS. THE ADVICE AND STRATEGIES CONTAINED HEREIN MAY NOT BE SUITABLE FOR YOUR SITUATION. YOU SHOULD CONSULT WITH A PROFESSIONAL WHERE APPROPRIATE. NEITHER THE PUBLISHER NOR THE AUTHOR SHALL BE LIABLE FOR DAMAGES ARISING HEREFROM.

For general information on our other products and services, please contact our Customer Care Department within the U.S. at 877-762-2974, outside the U.S. at 317-572-3993, or fax [phone]. For technical support, please visit www.wiley.com/techsupport.

Wiley publishes in a variety of print and electronic formats and by print-on-demand. Some material included with standard print versions of this book may not be included in e-books or in print-on-demand. If this book refers to media such as a CD or DVD that is not included in the version you purchased, you may download this material at http://booksupport.wiley.com. For more information about Wiley products, visit www.wiley.com.

Library of Congress Control Number: 2013954199

ISBN 978-1-118-82741-3 (pbk); ISBN 978-1-118-82746-8 (ebk); ISBN 978-1-118-82757-4 (ebk)

Manufactured in the United States of America

10 9 8 7 6 5 4 3 2 1

Trigonometry For Dummies®, 2nd Edition

Visit www.dummies.com/cheatsheet/trigonometry to view this book's cheat sheet.

Table of Contents

Introduction

About This Book

Foolish Assumptions

Icons Used in This Book

Beyond the Book

Where to Go from Here

Part I: Getting Started with Trigonometry

Chapter 1: Trouncing Trig Technicalities

Taking Trig for a Ride: What Trig Is

Sizing up the basic figures

Angling for position

Triangulating your position

Circling the wagons

Understanding Trig Speak

Defining trig functions

Taming the radicals

Equating and Identifying

Graphing for Gold

Describing graphing scales

Recognizing basic graphs

Chapter 2: Coordinating Your Efforts with Cartesian Coordinates

Starting Out Simple: Plotting Points

Axes, axes, we all fall down

Determining the origin of it all

Plotting x versus y

Cutting the graph into four parts

From Here to There: Calculating Distances

Counting on vertical and horizontal distances

Another slant: Diagonal distances

Using exact values or estimating distances

Getting to the Center of It All

Finding the midpoint of a line segment

Locating the center of a circle

Partitioning line segments further

Pinpointing the center of a triangle

Racing Down the Slope

Slaloming slope formula

Recognizing parallel and perpendicular lines

Defining Circles with Numbers

Centering circles at the origin

Wandering centers

Chapter 3: Functioning Well

Relations versus Functions

Function junction, what's your function?

Using function notation

Determining domain and range

In-Verse Functions: Rhyme or Reason?

Which functions have inverses?

Finding an inverse function

Transforming Functions

Translating a function

Reflecting like a mirror

Chapter 4: Getting Your Degree

Angles, Angles Everywhere: Measuring in Degrees

Slicing a coordinate plane

Looking elsewhere for degree measures

Graphing Angles in Standard Position

Positioning initial and terminal sides

Measuring by quadrants

What's Your Angle? Labeling in Various Ways

Using negative angle measures

Comingling with coterminal angles

Renaming angles: So many aliases

Chapter 5: Dishing Out the Pi: Radians

What's in a Radian?

Relating to a circle

Converting degrees and radians

Highlighting favorites

Making a Clone of Arc

Taking chunks out of circles

Sweeping hands

Going out and about

Chapter 6: Getting It Right with Triangles

Sizing Up Right Triangles

What's so right about them?

The anatomy of a right triangle

Pythagoras Schmythagoras: Demystifying the Pythagorean Theorem

Hitting a Pythagorean triple

Solving for a missing length

In a League of Their Own: Special Right Triangles

30-60-90 right triangles

Isosceles right triangles

Part II: Trigonometric Functions

Chapter 7: Doing Right by Trig Functions

SohCahToa to the Rescue: How Trig Functions Work

The name game: A right triangle's three sides

The six ratios: Relating the three sides

The sine function: Opposite over hypotenuse

The cosine function: Adjacent over hypotenuse

The tangent function: Opposite over adjacent

All together, now: Using one function to solve for another

Similar right triangles within a right triangle

Socking the rules away: The legend of SohCahToa

Taking It a Step Further: Reciprocal Functions

The cosecant function: Sine flipped upside down

The secant function: Cosine on its head

The cotangent function: Tangent, tails side up

Angling In on Your Favorites

Identifying the most popular angles

Determining the exact values of functions

Chapter 8: Trading Triangles for Circles: Circular Functions

Getting Acquainted with the Unit Circle

Placing points on the unit circle

Finding a missing coordinate

Sticking to rational coordinates

Going Full Circle with the Angles

Staying positive

Being negative or multiplying your angles

Locating and computing reference angles

Chapter 9: Defining Trig Functions Globally

Defining Trig Functions for All Angles

Putting reference angles to use

Labeling the optimists and pessimists

Combining all the rules

Using Coordinates of Circles to Solve for Trig Functions

Calculating with coordinates on the unit circle

Calculating with coordinates on any circle at the origin

Defining Domains and Ranges of Trig Functions

Friendly functions: Sine and cosine

Close cousins of their reciprocals: Cosecant and secant

Brothers out on their own: Tangent and cotangent

Chapter 10: Applying Yourself to Trig Functions

First Things First: Elevating and Depressing

Measuring Tall Buildings with a Single Bound

Rescuing a damsel from a tower

Determining the height of a tree

Measuring the distance between buildings

Measuring Slope

The Sky's (Not) the Limit

Spotting a balloon

Tracking a rocket

Measuring the view of satellite cameras

Calculating Odd Shapes and Maneuvering Corners

Finding the area of a triangular piece of land

Using Heron's Formula

Moving an object around a corner

Part III: Identities

Chapter 11: Identifying Basic Identities

Flipping Functions on Their Backs: Reciprocal Identities

Function to Function: Ratio Identities

Opposites Attract: Opposite-Angle Identities

Revisiting the Classic Theorem: Pythagorean Identities

The mother of all Pythagorean identities

Extending to tangent and secant

Finishing up with cotangent and cosecant

Rearranging the Pythagorean identities

Combining the Identities

The many faces of sine

Working out the versions

Chapter 12: Operating on Identities