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

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Circular Functions


Preface edit

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 Functions edit

Sin edit

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.

Cos edit

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.

Tan edit

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.

Arcsin edit

Also known as   or  

Arccos edit

Also known as   or  

Arctan edit

Also known as   or  

Examples edit

Graphing Functions edit

General Method edit

Trigonometric Functions Method edit
Reciprocal Trigonometric Functions Method edit
Inverse Trigonometric Functions Method edit

Sin edit

Cos edit

Tan edit

Arcsin edit

Arccos edit

Arctan edit