IB Maths AA 3.8 Definitions

This page contains our IB Maths AA definitions for 3.8. By learning each one of these definitions, you will fully cover the content for IB Maths AA 'Advanced trigonometry'.

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

arccos

The inverse function of cosine that returns the principal angle '

y

' such that '

\cos y=x

', with domain '

-1\leq x\leq1

' and output values '

0\leq y\leq\pi

arcsin

An inverse trigonometric function whose derivative is

\frac{d}{dx}\left(\arcsin x\right)=\frac{1}{\sqrt{1-x^2}}

, and for an input

f(x)

becomes

\frac{f'(x)}{\sqrt{1-\left(f(x)\right)^2}}

arctan

The inverse function of tangent that returns the principal angle '

y

' such that '

\tan y=x

', with domain all real numbers and output values '

-\frac{\pi}{2}\lt y\lt\frac{\pi}{2}

cosec

A reciprocal trigonometric ratio defined by '

\cosec x=\frac{1}{\sin x}

', so it is undefined where '

\sin x=0

cot

A reciprocal trigonometric function whose derivative is

\frac{d}{dx}\left(\cot x\right)=-\cosec^2 x

, and for an input

f(x)

becomes

-\cosec^2\left(f(x)\right)f'(x)

domain

The set of input values for which a model is intended to be used, chosen using the context rather than only the algebraic definition.

range

The set of possible outputs a function can produce.

sec

A reciprocal trigonometric function whose derivative is

\frac{d}{dx}\left(\sec x\right)=\sec x\tan x

; for an input

f(x)

\frac{d}{dx}\left(\sec\left(f(x)\right)\right)=\sec\left(f(x)\right)\tan\left(f(x)\right)f'(x)

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