IB Maths AI 3.7 Definitions

This page contains our IB Maths AI definitions for 3.7. By learning each one of these definitions, you will fully cover the content for IB Maths AI 'Unit circle'.

All Topic 3 Sub-topics 3.1: Fundamentals Of Geometry 3.2: Introduction To Trigonometry 3.3: Applied Trigonometry 3.4: Circles 3.5: Perpendicular Bisectors 3.6: Voronoi Diagrams (HL)3.7: Unit circle (HL)3.8: Geometric transformations (HL)3.9: Vectors (HL)3.10: Vector lines (HL)3.11: Graph theory (HL)3.12: Adjacency matrices (HL)3.13: Algorithms & problems

ambiguous case

The situation when two sides and a non-included angle are given for a triangle, where using the sine rule can lead to no triangle, one triangle, or two different triangles because

\sin\theta=\sin\left(\pi-\theta\right)

cos

A trigonometric function whose derivative is '

-\sin x

even function

A function with symmetry in the

y

-axis, satisfying

f\left(-x\right)=f\left(x\right)

, for example

\cos\left(-x\right)=\cos x

odd function

A function with rotational symmetry about the origin, satisfying

f\left(-x\right)=-f\left(x\right)

, for example

\sin\left(-x\right)=-\sin x

and

\tan\left(-x\right)=-\tan x

quadrant

One of the four regions of the coordinate plane determined by the

x

- and

y

-axes, used to determine the signs of

\sin\theta

\cos\theta

, and

\tan\theta

reference angle

The acute angle between the terminal side of an angle and the

x

-axis, used with quadrant signs to find exact trigonometric values.

sin

A trigonometric function whose derivative is '

\cos x

sine rule

A relationship for any triangle with sides

a

b

c

opposite angles

A

B

C

\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}

tan

Defined by

\tan\theta=\frac{\sin\theta}{\cos\theta}

, so it is undefined whenever

\cos\theta=0

unit circle

A circle of radius

1

centred at the origin, with equation

x^2+y^2=1

, used to define trigonometric functions for any angle.

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