# 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