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

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Mechanics Practice SACS


Preface[edit]

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

Formulae[edit]

Ellipses, Circles and Hyperbolas[edit]

Ellipses[edit]

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.

Circles[edit]

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 .

Hyperbolas[edit]

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 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