VCE Specialist Mathematics/Units 3 and 4: Specialist Mathematics/Formulae

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PrefaceEdit

This is a list of all formulae needed for Units 3 and 4: Specialist Mathematics.

FormulaeEdit

Ellipses, Circles and HyperbolasEdit

EllipsesEdit

General formula:

  •  

General Notes:

  • Point   defines the ellipses center.
  • Points   defines the ellipses domain, and horizontal endpoints - i.e. horizontal stretch.
  • Points   defines the ellipses range, and vertical endpoints - i.e. vertical stretch.

CirclesEdit

General formula:

  •  

General Notes:

  • Point   defines the circles center.
  • Points   defines the circles domain - i.e. stretch.
  • Points   defines the circles range - i.e. stretch.
  • A circle is a subset of an ellipse, such that  .

HyperbolasEdit

General formulae:

  •  
  •  

General Notes:

  • Point   defines the hyperbolas center.
  • Points   defines the hyperbolas domain,  .
  • The switch in positions of the fractions containing x and y, indicate the type of hyperbola - i.e. vertical or horizontal. The hyperbola is horizontal in the first, and negative in the second of the General hyperbolic formulae above.
  • Graphs   defines the hyperbolas domain  .

Trignometric 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