# HSC Extension 1 and 2 Mathematics/Trigonometric functions

From Wikibooks, open books for an open world

## Contents

- 1 Radian measure of an angle
- 2 Arc length and area of a sector of a circle
- 3 Area of a segment of a circle
- 4 Definitions of trigonometric functions
- 5 Symmetry properties of trigonometric functions
- 6 Some exact values
- 7 Graphs of trigonometric functions
- 8 Graphs of y = a sin bx and y = a cos bx
- 9 Graphs of y = a sin b(x + c) and y = a cos b(x + c)
- 10 Graphical solution of equations
- 11 Derivative of sin x and cos x
- 12 Derivative of tan x
- 13 Derivative of sin (ax + b)
- 14 Derivative of cos (ax + b)
- 15 Functions defined by integrals (indefinite integrals)
- 16 Primitives of 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.