Trigonometry/Trigonometric Analysis

Welcome to the Lesson of Analytical Trigonometry
Part of the School of Olympiads

This topic deals with the analytical aspects of Trigonometry. Widely this topic covers Trigonometric Identities and Equations. And important part of this topic is trigonometry through Complex Numbers by the use of De Moivre's Law and its application.

Function Inverse function Reciprocal Inverse reciprocal
sine sin arcsine arcsin cosecant csc arccosecant arccsc
cosine cos arccosine arccos secant sec arcsecant arcsec
tangent tan arctangent arctan cotangent cot arccotangent arccot

Theorems edit

Identities edit

Basic Relationships edit

Pythagorean trigonometric identity  
Ratio identity  

Each trigonometric function in terms of the other five.

Historic Shorthands
Name(s) Abbreviation(s) Value
versed sine, versine  
versed cosine, vercosine,
coversed sine, coversine
haversed sine, haversine  
haversed cosine, havercosine,
hacoversed sine, hacoversine,
cohaversed sine, cohaversine
exterior secant, exsecant    
exterior cosecant, excosecant    

Reflected in   Reflected in  
(co-function identities)
Reflected in  

Periodicity and Shifts
Shift by π/2 Shift by π
Period for tan and cot
Shift by 2π
Period for sin, cos, csc and sec

Angle Sum Identities edit

Complex Numbers, De Moivre's Law and Argand Plane edit

Examples edit

Resources edit

Textbooks edit

Practice Questions edit







Related WebApps edit

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