Mind Map Gallery Trigonometry Concept Map
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Trigonometry Concept Map
This is a concept map about "Trigonometry". You can easily create your own mind map with EdrawMind.
Edited at 2020-12-23 09:17:06
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Trigonometry Concept Map
Trigonometrical Ratios
Ratios
Tangent (tan)
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.