HSC Extension 1 and 2 Mathematics/Trigonometric functions

Radian measure of an angle
2π radians in a revolution

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

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