[<< wikibooks] HSC Extension 1 and 2 Mathematics/Trigonometric functions
== Radian measure of an angle ==
2π radians in a revolution


== Arc length and area of a sector of a circle ==

  
    
      
        l
        =
        r
        θ
        
      
    
    {\displaystyle l=r\theta \;}
  

  
    
      
        A
        =
        
          
            1
            2
          
        
        
          r
          
            2
          
        
        θ
      
    
    {\displaystyle A={\frac {1}{2}}r^{2}\theta }
  

Where θ is in radians


== Area of a segment of a circle ==


=== Minor segment ===

  
    
      
        A
        =
        
          
            1
            2
          
        
        
          r
          
            2
          
        
        (
        θ
        −
        sin
        ⁡
        θ
        )
      
    
    {\displaystyle A={\frac {1}{2}}r^{2}(\theta -\sin \theta )}
  

Where θ is in radians


=== Major segment ===

  
    
      
        A
        =
        π
        
          r
          
            2
          
        
        −
        
          
            1
            2
          
        
        
          r
          
            2
          
        
        (
        θ
        −
        sin
        ⁡
        θ
        )
      
    
    {\displaystyle A=\pi r^{2}-{\frac {1}{2}}r^{2}(\theta -\sin \theta )}
  

Where θ is in radians


== Definitions of trigonometric functions ==
In mathematics, the trigonometric functions (also called circular functions) are functions of an angle. They are used to relate the angles of a triangle to the lengths of the sides of a triangle. Trigonometric functions are important in the study of triangles and modeling periodic phenomena, among many other applications.


== Symmetry properties of trigonometric functions ==


== Some exact values ==


== Graphs of trigonometric functions ==


== Graphs of y = a sin bx and y = a cos bx ==


== Graphs of y = a sin b(x + c) and y = a cos b(x + c) ==


== Graphical solution of equations ==


== Derivative of sin x and cos x ==

  
    
      
        
          sin
          ′
        
        ⁡
        x
        =
        cos
        ⁡
        x
        
      
    
    {\displaystyle \sin 'x=\cos x\;}
  

  
    
      
        
          cos
          ′
        
        ⁡
        x
        =
        −
        sin
        ⁡
        x
        
      
    
    {\displaystyle \cos 'x=-\sin x\;}
  


== Derivative of tan x ==

  
    
      
        
          tan
          ′
        
        ⁡
        x
        =
        
          sec
          
            2
          
        
        ⁡
        x
        
      
    
    {\displaystyle \tan 'x=\sec ^{2}x\;}
  


== Derivative of sin (ax + b) ==

  
    
      
        
          sin
          ′
        
        ⁡
        (
        a
        x
        +
        b
        )
        =
        a
        cos
        ⁡
        (
        a
        x
        +
        b
        )
        
      
    
    {\displaystyle \sin '(ax+b)=a\cos(ax+b)\;}
  


== Derivative of cos (ax + b) ==

  
    
      
        
          cos
          ′
        
        ⁡
        (
        a
        x
        +
        b
        )
        =
        −
        a
        sin
        ⁡
        (
        a
        x
        +
        b
        )
        
      
    
    {\displaystyle \cos '(ax+b)=-a\sin(ax+b)\;}
  


== Functions defined by integrals (indefinite integrals) ==


== Primitives of trigonometric functions ==


=== Approximate integration ===