Trigonometry

Title Page
Copyright Page
Table of Contents
Introduction
	About This Book
	Foolish Assumptions
	Icons Used in This Book
	Beyond the Book
	Where to Go from Here
Part 1 Getting Started with Trigonometry
	Chapter 1 Taking On Trig Technicalities
		Taking Trig for a Ride: What Trig Is
			Sizing up the basic figures
				Drawing segments, rays, and lines
				Intersecting lines
			Identifying angles and their names
				Naming angles by size
				Naming angles by letters
			Taking on triangles and their angles
				Angles in triangles
				Naming triangles by their shape
			Going outside the triangle
			Making a circle work from every angle
				Radius, diameter, circumference, and area
				Chord versus tangent
			Looking at angles in a circle
				Central angle
				Inscribed angle
				Interior angle
				Exterior angle
				Sectioning sectors
		Understanding Trig Speak
			Making the words fit the triangle
				Interpreting trig abbreviations
				Noting notation
				Functioning with angles
			Making triangles less radical
				Simplifying radical forms
				Approximating answers
		Equating and Identifying
		Finding Trig Applications in the Basics
			Measuring fencing
			Ptolemy’s Theorem
			Dealing with radicals
			Skateboarding
	Chapter 2 Cooperating 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
				The Pythagorean Theorem
				Determining 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
		Circling Around with Applications
			Spinning a wheel
			Containing the cattle
	Chapter 3 Finding Degrees in Triangles and Planes
		Angles, Angles Everywhere: Measuring in Degrees
			Slicing a coordinate plane
			Looking elsewhere for degree measures
				Navigating with degrees
				Understanding Norm’s workshop
		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
				More than one revolution
				Negative coterminal angles
			Renaming angles: So many aliases
		Making Degrees Work for You
			Moon shining
			Games people play
	Chapter 4 Dishing Out the Pi: Radians
		What’s in a Radian?
			Relating to a circle
			Converting degrees and radians
				Changing degrees to radians
				Changing radians to degrees
			Highlighting favorites
		Making a Clone of Arc
			Taking chunks out of circles
				Scanning with a radar
				Sharing pizza
			Sweeping hands
				Riding the minute hand
				Riding the Ferris wheel
			Going out and about
				Measuring the distance to the moon
				Racing around the track
	Chapter 5 Tackling Right Triangles
		Sizing Up Right Triangles
			What’s so right about them?
			The anatomy of a right triangle
		Demystifying the Pythagorean Theorem
			Hitting a Pythagorean triple
			Solving for a missing length
				Practicing on triangles
				Finding the distance across a pond
		In a League of Their Own: Special Right Triangles
			30-60-90 right triangles
			Isosceles right triangles
		Getting the Applications Right
			How tall is your house?
			Beachfront measure
Part 2 Trigonometric Functions
	Chapter 6 Describing Trig Functions
		Discovering 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
		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
				A quick table for the three basic trig functions
				A quick table for the three reciprocal trig functions
		Building a Shorter Route
	Chapter 7 Relating Triangles to 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
				Figuring the angle measure in degrees
				Figuring the angle measure in radians
		Navigating with Circular Measures
			Introducing the compass
			Cycling with a cyclic quadrilateral
	Chapter 8 Taking Trig Functions Global
		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
				Domains of sine and cosine
				Ranges of sine and cosine
			Close cousins of their reciprocals: Cosecant and secant
				Domains of cosecant and secant
				Ranges of cosecant and secant
			Brothers out on their own: Tangent and cotangent
				Domains of tangent and cotangent
				Ranges of tangent and cotangent
		Applying the Trig Functions
			Flying around on a Ferris wheel
			Trying out some new trig functions
	Chapter 9 Applying Yourself to Trig Functions
		First Things First: Elevating and Depressing
		Measuring Tall Buildings with a Single Bound
			Rescuing a child from a burning building
			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 3 Identities
	Chapter 10 Introducing 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
				Changing sin2θ + cos2θ = 1
				Adjusting tan2θ + 1 = sec2θ
				Reconfiguring 1 = cot2θ = csc2θ
		Combining the Identities
			The many faces of sine
			Working out the versions
				Changing sine to cosine
				Changing sine to tangent
				Changing sine to cotangent
				Changing sine to secant
				Changing sine to cosecant
	Chapter 11 Operating on Identities
		Summing It Up
		Overcoming the Differences
		Doubling Your Money
			One plus one equals two sines
			Three’s a crowd
		Halving Fun Yet?
			Explaining the ±
			Half a tangent is double the fun
			Using half-angle identities
		Comparing Exact Values and Estimations
	Chapter 12 Proving Identities: The Basics
		Lining Up the Players
		Picking Sides
		Working on Both Sides
		Going Back to Square One
			Changing to sines and cosines
			Factoring
			Using a little bit of both
	Chapter 13 Sleuthing Out Identity Solutions
		Fracturing Fractions
			Breaking up is hard to do
			Finding a common denominator
		Using Tricks of the Trig Trade
			Multiplying by a conjugate
			Squaring both sides
		Identifying with the Operations
			Adding it up
			What difference does it make?
			Multiplying your fun
			Halving fun, wish you were here
		Applying the Magic of Trigonometry
			Making some given information work
			Off on a tangent
Part 4 Equations and Applications
	Chapter 14 Investigating Inverse Trig Functions
		Writing It Right
			Using the notation
				Interpreting the exponent
				Alternating the notation
			Distinguishing between the few and the many
		Determining Domain and Range of Inverse Trig Functions
			Inverse sine function
			Inverse cosine function
			Inverse tangent function
			Inverse cotangent function
			Inverse secant function
			Inverse cosecant function
			Summarizing domain and range
	Chapter 15 Making Inverse Trig Work for You
		Working with Inverses
		Getting Friendly with Your Calculator
			Changing the mode
			Interpreting notation on the calculator screen
				Using the inverse function button
				Calculating the inverse of a reciprocal function
				Working around the inverse cotangent
		Multiplying the Input
		Solving Some Mixed Problems
		Finding an Unknown Angle
	Chapter 16 Solving Trig Equations
		Generating Simple Solutions
		Factoring In the Solutions
			Finding a greatest common factor
			Factoring quadratics
			Increasing the degrees in factoring
			Factoring by grouping
		Using the Quadratic Formula
		Incorporating Identities
		Finding Multiple-Angle Solutions
		Squaring Both Sides
		Multiplying Through
		Solving with a Graphing Calculator
	Chapter 17 Obeying the Laws and Applying Them
		Describing the Parts of Triangles
			Standardizing the parts
			Determining a triangle
				Finding the one and only
				Dealing with the ambiguous case
		Following the Law of Sines
		Continuing with the Law of Cosines
			Defining the law of cosines
			Law of cosines for SAS
			Law of cosines for SSS
			Being ambiguous
		Finding the Areas of Triangles
			Finding area with base and height
			Finding area with three sides
			Finding area with SAS
			Finding area with ASA
Part 5 The Graphs of Trig Functions
	Chapter 18 Graphing Sine and Cosine
		The ABCs of Graphing
		Waving at the Sine
			Describing amplitude and period
				Gaining height with the amplitude
				Punctuating with the period
			Formalizing the sine equation
			Translating the sine
				Sliding up or down
				Shifting left or right
		Graphing Cosine
			Comparing cosine to sine
			Using properties to graph cosine
		Applying the Sines of the Times
			Sunning yourself
			Averaging temperature
			Taking your temperature
			Making a goal
			Theorizing with biorhythms
	Chapter 19 Graphing Tangent and Cotangent
		Checking Out Tangent
			Determining the period
			Assigning the asymptotes
			Fiddling with the tangent
				Multiplying the tangent
				Multiplying the angle
				Adding to tangent
		Confronting the Cotangent
	Chapter 20 Graphing Two More Trig Functions
		Seeing the Cosecant for What It Is
			Identifying the asymptotes
			Using the sine graph
			Varying the cosecant
		Unveiling the Secant
			Determining the asymptotes
			Sketching the graph of secant
			Fooling around with secant
		Laying Out the Inverse Functions
			Graphing inverse sine and cosine
			Taking on inverse tangent and cotangent
			Crafting inverse secant and cosecant
	Chapter 21 Topping Off Trig Graphs
		The Basics of Trig Equations
			Flipping over a horizontal line
			Interpreting the equation
				A is for amplitude
				B is for becoming (the period)
				C is for cruisin’ left or right
				D is for distancing yourself up or down
		Graphing with the General Form
		Adding and Subtracting Functions
		Applying Yourself to the Task
			Measuring the tide
			Tracking the deer population
			Measuring the movement of an object on a spring
Part 6 The Part of Tens
	Chapter 22 Ten Basic Identities . . . Plus Some Bonuses
		Reciprocal Identities
			Reciprocating the sine
			Checking in with the cosine
			Off on a tangent with its reciprocal
		Ratio Identities
			Creating the ratio identity for tangent
			Making the cotangent a ratio identity
		Pythagorean Identity Plus
		Opposite-Angle Identities
		Multiple-Angle Identities
			Going multiple with sine
			Cosine cooperates
			Tangent keeps its fractional origin
	Chapter 23 Ten Not-So-Basic Identities
		Product-to-Sum Identities
		Sum-to-Product Identities
		Reduction Formula
		Mollweide’s Equations
Appendix: Graphs and Function Values
	The Six Basic Trigonometric Functions and Their Graphs
	Trig Values of the Most Commonly Used Functions
	Trig Values of the Most Commonly Used Functions (Continued)
	Calculator Usage
Index
EULA