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

${\sin }^{\prime }x=\cos x$

${\cos }^{\prime }x=-\sin x$

Derivative of tan x

${\tan }^{\prime }x={\sec }^{2}x$

Derivative of sin (ax + b)

${\sin }^{\prime }(ax+b)=a\cos (ax+b)$

Derivative of cos (ax + b)

${\cos }^{\prime }(ax+b)=-a\sin (ax+b)$