VCE Specialist Mathematics/Units 3 and 4: Specialist Mathematics/Circular Functions

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PrefaceEdit

Formal Definition: 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.

Translation: Understanding the various functions that can be applied to and taken from (graphs) the unit circle, and includes recognizing and using the various algebraic identities to manipulate trigonometric functions and equations.

Graphing FunctionsEdit

SinEdit

General formula:

  •  

General Notes:

  • General formula achieved isolating the coefficient of x (n), i.e. the "lonely x rule".
  • A period is equal to  
  • The domain, unless restricted, is  
  • The range is equal to  , as the range of  , see unit circle.
  • The horizontal translation of   is reflected in the x-intercepts.

CosEdit

General formula:

  •  

General Notes:

  • General formula achieved isolating the coefficient of x (n), i.e. the "lonely x rule".
  • The domain, unless restricted, is  , as  
  • A period is equal to  , as the factor of n
  • The range is equal to  , as the range of  , see unit circle.
  • The horizontal translation of   is reflected in the x-intercepts.

TanEdit

General formula:

  •  

General Notes:

  • General formula achieved isolating the coefficient of x (n), i.e. the "lonely x rule".
  • A period is equal to  
  • The domain,  , as  , indicating the asymptotes.
  • The range, unless restricted, is  , as the range of  , see unit circle.
  • The horizontal translation of   is reflected in the x-intercepts.

ArcsinEdit

Also known as   or  

ArccosEdit

Also known as   or  

ArctanEdit

Also known as   or  

ExamplesEdit

Graphing FunctionsEdit

General MethodEdit

Trigonometric Functions MethodEdit
Reciprocal Trigonometric Functions MethodEdit
Inverse Trigonometric Functions MethodEdit

SinEdit

CosEdit

TanEdit

ArcsinEdit

ArccosEdit

ArctanEdit