HSC Extension 1 and 2 Mathematics/Trigonometric functions

Radian measure of an angleEdit

2π radians in a revolution

Arc length and area of a sector of a circleEdit



  • Where θ is in radians

Area of a segment of a circleEdit

Minor segmentEdit


  • Where θ is in radians

Major segmentEdit


  • Where θ is in radians

Definitions of trigonometric functionsEdit

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 functionsEdit

Some exact valuesEdit

Graphs of trigonometric functionsEdit

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

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

Graphical solution of equationsEdit

Derivative of sin x and cos xEdit



Derivative of tan xEdit


Derivative of sin (ax + b)Edit


Derivative of cos (ax + b)Edit


Functions defined by integrals (indefinite integrals)Edit

Primitives of trigonometric functionsEdit

Approximate integrationEdit