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

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## Contents

## 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