HSC Extension 1 and 2 Mathematics/Trigonometric functions

Radian measure of an angle edit

2π radians in a revolution

Arc length and area of a sector of a circle edit

 

 

  • Where θ is in radians

Area of a segment of a circle edit

Minor segment edit

 

  • Where θ is in radians

Major segment edit

 

  • Where θ is in radians

Definitions of trigonometric functions edit

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.

Symmetry properties of trigonometric functions edit

Some exact values edit

Graphs of trigonometric functions edit

Graphs of y = a sin bx and y = a cos bx edit

Graphs of y = a sin b(x + c) and y = a cos b(x + c) edit

Graphical solution of equations edit

Derivative of sin x and cos x edit

 

 

Derivative of tan x edit

 

Derivative of sin (ax + b) edit

 

Derivative of cos (ax + b) edit

 

Functions defined by integrals (indefinite integrals) edit

Primitives of trigonometric functions edit

Approximate integration edit