Differences Between Logarithmic and Trigonometric Term

The mathematical expressions for logarithm and trigonometry looks similar.

Logarithm expression: Log A

Trigonometric expression: Cos A
(this has been randomly chosen; Sin A and Tan A is equally fine).

Both are numbers operated upon to give another meaning. However, they have their differences.

Logarithm

The number operated upon is pure number and is related to indices. That is, x^y = A

The main objective of "logarithming" is to find the power to a number (base).

Its application is more towards algebraic manipulation converting number to number in another form (power to base, and vice versa).

Another application is to determine the number of digits needed to get a desired number (this may be in digital electronics where the number of bits is needed to form a certain number of counts ==> 2ⁿ = 10 , logarithm is needed to find "n").

Trigonometry

The number operated upon is angle and is related to length.

The main objectives of trigonometric operations are to determine the amplitude of height of a frequency component and the lengths of the side of a triangle formed by the defined angle.

The result of doing a trigonometric function is a ratio of 2 lengths of a triangle. It translates angle information to information of the number ratio (of 2 sides).

Formula

Log (XY) = Log X + Log Y

Cos (A + B) = Cos A Cos B - Sin A Sin B

The formulae above are quoted to reflect the similarity but with slight differences.

Note that "Log" is with (XY) and "Cos" is with (A + B).

We should be careful not to inter-mix the concept and formulae as they serve different purposes.
This is the fun part in maths. The challenge of recognising the format and meaning is the other exciting part.

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