Trigonometry Concept Map

Trigonometry Concept Map
Trigonometrical Ratios
Ratios
Tangent (tan)
TOA: Opposite/ Adjacent. The ratio is known as
the tangent of angle a.
Cosine (cos)
CAH: Adjacent/ Hypotenuse. The ratio is
known as the cosine of angle a.
Sine (sin)
SOH: Opposite/ Hypotenuse. The ratio is known
as the sine of angle a.
TOA CAH SOH: 'Big Fat Lady' in Hokkien
Concepts
Mathematical Concepts
Constancy
With the angle being fixed, the equality of
value of each trigonometrical ratio is
maintained regardless of size of triangle.
Patterns
By recognizing and understanding
patterns, we can make logical deductions
and justify our conclusion.
Relationships
Trigonometrical ratios depict the
relationship amongst the sides and
angles of a triangle.
Trigonometry
Definition
A branch of mathematics that studies triangles and the
relationships between their sides and the angles between these
sides.
Application
Ancient times: Used in measurement of heights
and distances of objects that could not be
otherwise measured (Eg. distance of stars from
Earth)
Present: Making quick and simple calculations
regarding height and distances of far away
objects (INDIRECT MEASUREMENT)
Pythagoras' Theorem
Theorems
1. Pythagoras' Theorem:
In a rightangled triangle, the
square of the hypothenuse is
equal to the sum of squares of
the other two sides.
Proof: The sum of the areas of the two squares on the
legs (a and b) equals the area of the square on the
hypotenuse.
2. Converse of Pythagoras' Theorem:
In a triangle, if the square of the
longest side is equal to the sum of
the squares of the remaining two
sides, then the angle opposite to
the longest side, is a right angle.
Proof
Concepts
Mathematical Concepts
Constancy
The equality of the equation representative of
Pythagoras' Theorem, does not change
regardless of the size of the triangle.
Relationship
Pythagoras' Theorem is a relationship of the size
of a rightangled triangle.
Shapes
Pythagoras' Theorem is a geometric
representation of an algebraic relation.
Macroconcepts
Models
Pythagoras' Theorem can be
represented geometrically and be used
to solve problems involving
2dimensional and 3dimensional
models, to solve real life problems
The converse of Pythagoras' Theorem
facilitates testing if a triangle is a rightangled
triangle.
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