Trigonometry Study Guide

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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