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Trigonometry functions


Trigonometry is a branch of mathematics that deals with triangles. It is more like geometry, but it deals particularly with right angle triangles. The concept of trigonometry deals with the relationship between angles and sides of the triangle. To accurately describe these relationships, we must first understand what the sides, angles and the functions that are used to establish relationships between them.

Consider the following right angle triangle:

Trigonometric triangle

Trigonometric functions


Sine function - defines the ratio of the opposite leg of the triangle to the hypotenuse. Thus in mathematical terms, this can be written as:
Cos A = Opposite / Hypotenuse = a / c


Cosine function - defines the ratio of the adjacent leg of the triangle to the hypotenuse. Thus in mathematical terms, this can be written as:
Sin A = Adjacent / Hypotenuse = b / c


Tangent function - defines the ratio of the opposite leg of the triangle to the Adjacent leg. Thus in mathematical terms, this can be written as:
Tan A = Opposite / Adjacent = a / b = Sin A / Cos A


Do not be intimidated by the Sin A / Cos A in the above formula, even though it looks complicated, it is really simple to understand. Here is how they arrived a that formula:
Sine A = a / c
Cos A = b / c

=> a / c ----------- b / c

=> a / c * c / b when dividing a fraction by another,
we simply turn the second fraction upside down and multiply it by
the first fraction.

=> a / c * c / b the c cancels out leaving us with
=> a / b


Do not worry too much for now just know the formulas and how they relate to the triangle. In the next few postings we will take a detailed look at how to calculate the size of an angle and length of sides using trigonometric functions.






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