TOA: Opposite/ Adjacent. The ratio is known asthe tangent of angle a.

Cosine (cos)

CAH: Adjacent/ Hypotenuse. The ratio isknown as the cosine of angle a.

Sine (sin)

SOH: Opposite/ Hypotenuse. The ratio is knownas the sine of angle a.

TOA CAH SOH: 'Big Fat Lady' in Hokkien

Concepts

Mathematical Concepts

Constancy

With the angle being fixed, the equality ofvalue of each trigonometrical ratio ismaintained regardless of size of triangle.

Patterns

By recognizing and understandingpatterns, we can make logical deductionsand justify our conclusion.

Relationships

Trigonometrical ratios depict therelationship amongst the sides andangles of a triangle.

Trigonometry

Definition

A branch of mathematics that studies triangles and therelationships between their sides and the angles between thesesides.

Application

Ancient times: Used in measurement of heightsand distances of objects that could not beotherwise measured (Eg. distance of stars fromEarth)

Present: Making quick and simple calculationsregarding height and distances of far awayobjects (INDIRECT MEASUREMENT)

Pythagoras' Theorem

Theorems

1. Pythagoras' Theorem:

In a rightangled triangle, thesquare of the hypothenuse isequal to the sum of squares ofthe other two sides.

Proof: The sum of the areas of the two squares on thelegs (a and b) equals the area of the square on thehypotenuse.

2. Converse of Pythagoras' Theorem:

In a triangle, if the square of thelongest side is equal to the sum ofthe squares of the remaining twosides, then the angle opposite tothe longest side, is a right angle.

Proof

Concepts

Mathematical Concepts

Constancy

The equality of the equation representative ofPythagoras' Theorem, does not changeregardless of the size of the triangle.

Relationship

Pythagoras' Theorem is a relationship of the sizeof a rightangled triangle.

Shapes

Pythagoras' Theorem is a geometricrepresentation of an algebraic relation.

Macroconcepts

Models

Pythagoras' Theorem can berepresented geometrically and be usedto solve problems involving2dimensional and 3dimensionalmodels, to solve real life problems

The converse of Pythagoras' Theoremfacilitates testing if a triangle is a rightangledtriangle.