# HSC Extension 1 and 2 Mathematics/Trigonometric functions

## Arc length and area of a sector of a circle

$l = r \theta \;$

$A = \frac{1}{2}r^2 \theta$

• Where θ is in radians

## Area of a segment of a circle

### Minor segment

$A = \frac{1}{2}r^2 ( \theta - \sin \theta )$

• Where θ is in radians

### Major segment

$A = \pi r^2 - \frac{1}{2}r^2 ( \theta - \sin \theta )$

• Where θ is in radians

## Definitions of trigonometric functions

In mathematics, the trigonometric functions (also called circular functions) are functions of an angle. They are used to relate the angles of a triangle to the lengths of the sides of a triangle. Trigonometric functions are important in the study of triangles and modeling periodic phenomena, among many other applications.

## Derivative of sin x and cos x

$\sin 'x = \cos x \;$

$\cos 'x = - \sin x \;$

## Derivative of tan x

$\tan 'x = \sec^2 x \;$

## Derivative of sin (ax + b)

$\sin '(ax + b) = a \cos (ax + b) \;$

## Derivative of cos (ax + b)

$\cos '(ax + b) = -a \sin (ax + b) \;$