Trigonometry Study Guide

Boost Your grades with this illustrated Study Guide. You will use it from high school all the way to graduate school and beyond.

Features

Clear and concise explanations
Difficult concepts are explained in simple terms
Illustrated with graphs and diagrams
Search for the words or phrases
Access the guide anytime, anywhere - at home, on the train, in the subway.
Use your down time to prepare for an exam.
Always have the guide available for a quick reference.


Table of Contents

Introduction: Overview | Basic definitions | Extending the definitions | Mnemonics | Pi | Radian

Trigonometric Function Definitions: Right triangle definitions | Unit-circle definitions

Trigonometric Identities: Notation | Periodicity, symmetry, and shifts | Linear combinations | Pythagorean identities | Angle sum and difference identities | Tangents of sums of finitely many terms | Sines and cosines of sums of infinitely many terms | Double-angle formulae | Triple-angle formulae | Multiple-angle formulae | Power-reduction formulae | Half-angle formulae | Product-to-sum identities | Ptolemy's theorem | Sum-to-product identities | Other sums of trigonometric functions | Inverse trigonometric functions | Trigonometric conversions | Infinite product formula | Relation to the Complex Exponential Function | Identities without variables | Exponential Definitions

Inverse Trigonometric Function: Relationships among the inverse trigonometric functions | General solutions | Recommended method of calculation | Two argument variant of arctangent | Logarithmic forms

Trigonometric Function Applications: Computation | Exact Trigonometric Constants | Law of sines | Law of cosines | Law of tangents

Periodic Functions: General definition | Antiperiodic functions and other generalizations | Amplitude | Frequency | Wavelength | Sine wave

Polar coordinate system: Plotting points with polar coordinates | Converting between polar and Cartesian coordinates | Polar equations | Circle | Line | Polar rose | Archimedean spiral | Conic sections | Complex numbers | Three dimensions | Cylindrical coordinates | Spherical coordinates | Applications

Spherical Trigonometry: Lines on a sphere | Law of Cosines and Law of Sines | Central Angle

Great-circle Distance: The formula | Spherical distance on the Earth | Spherical coordinates | Haversine Formula