Fundamental Mathematics/Trigonometry

AnglesEdit

 

When two lines AB and AC cuts at one point A , angle is formed at point A between AB and AC . Angle is denoted as   . Angle is measured in Degree (o) or Radian (Rad) .

 
 

To convert degrees to radians:

 

To convert radians to degrees:

 

Trigonometric functionsEdit

Fundamental trigonometric functionsEdit

Relation of right triangle sides are defined as trigonometric functions. They are:

Trignometric Function Definition Mathematical Formula Graphs
Sine Ratio of opposite side over hypotnuse    
Cosine Ratio of adjacent side over hypotnuse    
Tangent Ratio of opposite over adjacent    
Cotangent Ratio of adjacent over opposite    
Secant Ratio of 1 over opposite    
Cosecant Ratio of 1 over adjacent    

ChracteristicsEdit

Periodic  
 
 
Symmetry
 
 
 
Phase shift
 
 
 
Complex Power
 
 
với  
 

 
de Moivre's formula:
 
Limit
 
 
Derivative
 
 

Trigonometric formulasEdit

Fundamental trigonometry functionEdit

 

Sum and difference anglesEdit

 
 
 

Reduced powerEdit

 
 
 
 
 

Half anglesEdit

 
 
 
 
 
 
 
 
 
        and       and    

Product of trigonomtric functionsEdit

 
 
 

Inverse trigonometric functionsEdit

 
 
 
 
 
 
 
 
 
 
 

Complex numberEdit

 
 
 

With

 

Hence

 

Infinite ProductEdit

 
 
 
 
 

LimitsEdit

 
 

DerivativesEdit

 
 
 
 
 
 
 
 

Common Trigonomtric functionsEdit

 
 
 
 
 
 
 
 
 
 
 
 

Double angle trigonometric functionsEdit

 
 
 

In general,

If Tn is Chebyshev n ordered then

 

De Moivre formula:

 

hạt nhân Dirichlet Dn(x) sẽ xuất hiện trong các công thức sau:

 
 
 
 

Triple angle trigonometric functionsEdit

 
 

SeriesEdit

 
 
 
 
 
 

IntegralsEdit

 
 
 
 
 
 

Complex trigonometric functionsEdit

 
 
 

Further readingEdit