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

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)

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