IB Maths AA 3.6 Definitions

This page contains our IB Maths AA definitions for 3.6. By learning each one of these definitions, you will fully cover the content for IB Maths AA 'Trigonometric identities'.

All Topic 3 Sub-topics 3.1: Fundamentals Of Geometry 3.2: Introduction To Trigonometry 3.3: Applied Trigonometry 3.4: Circles 3.5: Unit Circle 3.6: Trigonometric Identities 3.7: Trigonometric Graphs (HL)3.8: Advanced trigonometry (HL)3.9: Compound angles (HL)3.10: Vectors (HL)3.11: Lines (HL)3.12: Planes

double angle identities

Formulae that express '

\sin 2x

' and '

\cos 2x

' in terms of '

\sin x

' and '

\cos x

', for example '

\sin 2x=2\sin x\cos x

' and '

\cos 2x=\cos^{2}x-\sin^{2}x=2\cos^{2}x-1=1-2\sin^{2}x

finite interval

A restricted range of values for the variable, such as '

0\le x\le2\pi

', within which all solutions to an equation must be found.

Identity

A square matrix with ones on the main diagonal and zeros elsewhere, with the property that

AI=IA=A

for any compatible matrix

A

Pythagorean identity

The fundamental relationship between sine and cosine given by '

\cos^{2}{\theta}+\sin^{2}{\theta}=1

', valid for all angles where the functions are defined.

quadratic form

A rearrangement where an equation becomes quadratic in a single trigonometric function, for example '

a\sin^{2}x+b\sin x+c=0

' (or similarly in '

\cos x

' or '

\tan x

'), allowing standard quadratic methods to be used.

quadratic formula

A method for solving '

au^{2}+bu+c=0

' by using '

u=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}

', often after substituting '

u=\sin x

', '

u=\cos x

' or '

u=\tan x

trigonometric identity

An equation involving trigonometric functions that is true for all values of the variable for which both sides are defined, and is used to simplify expressions, prove results, and solve equations.

Next Up

You have completed the topic 3 definitions for IB Maths AA - continue with related resources below or explore the full IB Maths AA course from the IBO.

Explored IB Maths AA Definitions?

Get stuck into one of our other subjects!

Other subjects' Definitions

Biology

Chemistry

Physics

Maths AI

Join 85,000 students, across 130+ countries, in 500+ IB schools. That's half of the IB science graduates worldwide.

Start a 7d free trial