HSC Extension 1 and 2 Mathematics/Trigonometric functions

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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]