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Table of Contents Introduction ......................................................................................................XX Pretest ...............................................................................................................XX Chapter 1: Trigonometric Ideas .................................................................................XX Angles and Quadrants ...................................................................................XX Coterminal Angles........................................................................................XX Trigonometric Functions of Acute Angles............................................................XX Introducing Trigonometric Identities...................................................................XX Reciprocal Trigonometric Functions.........................................................XX Trigonometric Cofunctions.....................................,...............................XX Two Special Triangles..........................................................................XX Trigonometric Functions of General Angles..........................................................XX Reference Angles..............................................................................XX Squiggly vs. Straight..........................................................................XX Trig Tables vs. Calculators.............................................................................XX Interpolation ...............................................................................XX Chapter 2: Graphs of Trigonometric Functions ................................................................XX Understanding Degree Measure............. ..............................................................XX Understanding Radian Measure ...........................................................................XX Relationships Between Degrees and Radians ...........................................................XX The Unit Circle and Circular Functions ..................................................................XX Domain vs. Range.............................................................................................XX Periodic Functions ........................................................................XX Graphs of the Trigonometric Functions ..................................................................XX Graphing Sine and Cosine .......................................................................XX Vertical Displacement and Amplitude..........................................................XX Frequency and Phase Shift.......................................................................XX Graphing Tangent..................................................................................XX Assymptotes........................................................................................XX Graphing Cosecant, Secant, and Cotangent ...................................................XX Chapter 3: Trigonometry of Triangles ............................................................................XX Finding Missing Parts of Right Triangles ........................................................................XX Angles of Elevation and Depression........................................................................XX The Law of Sines .............................................................................................XX The Law of Cosines ..........................................................................................XX Solving General Triangles....................................................................................XX SSS...................................................................................................XX SAS...................................................................................................XX ASA................................................................................................XX SAA................................................................................................XX SSS...................................................................................................XX SSA, The Ambiguous Case......................................................................XX Areas of Triangles..............................................................................................XX Area for SAS.......................................................................................XX Area for ASA or SAA ............................................................................XX Heron's Formula (SSS) .............................................................................XX Chapter 4: Trigonometric Identities .................................................................................XX Fundamental Identities ......................................................................................XX Reciprocal Identities ..............................................................................XX Ratio Identities ....................................................................................XX Cofunction Identities .............................................................................XX Identities for Negatives...........................................................................XX Pythagorean Identities ..........................................................................XX Addition and Subtraction Identities ........................................................................XX Double Angle Identities ......................................................................................XX Half Angle Identities .........................................................................................XX Tangent Identities .............................................................................................XX Product-Sum and Sum-Product Identities ...............................................................XX Product-Sum Identities...........................................................................XX Sum-Product Identities ................ ...............................................XX Chapter 5: Vectors .....................................................................................................XX Vectors vs. Scalars ............................................................................................XX Vector Addition Triangle ....................................................................................XX Tail-to-Tip Rule....................................................................................XX Parallelogram of Forces .....................................................................................XX Vectors in the Rectangular Coordinates System ........................................................XX Resolution of Vectors.....................................................................................XX Algebraic Vector Addition ................................................................................XX Scalar Multiplication ........................................................................................XX Dot Products..................................................................................................XX Chapter 6: Polar Coordinates and Complex Numbers ..........................................................XX Polar Coordinates ...........................................................................................XX Converting Between Polar and Rectangular Coordinates..............................................XX Converting from Polar to Rectangular Coordinates..........................................XX Converting from Rectangular to Polar Coordinates..........................................XX Some Showy Polar Graphs.................................................................................XX Plotting Complex Numbers on Rectangular Axes .......................................................XX Plotting Complex Numbers on the Polar Axis...........................................................XX Conjugates of Complex Numbers ........................................................................XX Multiplying and Dividing Complex Numbers...........................................................XX Finding Powers of Complex Numbers.....................................................................XX Chapter 7: Inverse Functions, Equations, and Motion ...........................................................XX Restricting Functions.........................................................................................XX Inverse Sine and Cosine .....................................................................................XX Inverse Tangent ........... .....................................................................................XX Inverses of Reciprocal Functions .............................................................................XX Trigonometric Equations.....................................................................................XX Uniform Circular Motion ....................................................................................XX Simple Harmonic Motion....................................................................................XX Customized Full Length Exam.......................................................................................XX Summary of Formulas .................................................................................................XX Table of Trigonometric Functions.................................................................................XX Glossary ..................................................................................................................XX Index.......................................................................................................................X X
Library of Congress Subject Headings for this publication:
Trigonometry -- Problems, exercises, etc.