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

VCE Specialist Mathematics Formulae Mechanics Practice SACS Preface This is a list of all formulae needed for Units 3 and 4: Specialist Mathematics. Formulae Ellipses, Circles and Hyperbolas Ellipses 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 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 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 Sin 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 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 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 Also known as or Arccos Also known as or Arctan Also known as or