HSC Extension 1 and 2 Mathematics/Trigonometric functions

Arc length and area of a sector of a circle

${\displaystyle l=r\theta \;}$

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

• Where θ is in radians

Area of a segment of a circle

Minor segment

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

• Where θ is in radians

Major segment

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

• 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

${\displaystyle \sin 'x=\cos x\;}$

${\displaystyle \cos 'x=-\sin x\;}$

Derivative of tan x

${\displaystyle \tan 'x=\sec ^{2}x\;}$

Derivative of sin (ax + b)

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

Derivative of cos (ax + b)

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