## Sunday, 10 August 2008

### Cos A - True Meaning Of Trigonometric Term

While studying for the trigonometry topics, did you wonder what this trigonometric term "cos A" really means?

You are told that Cos A = a number.

But is that all?

(Note in this post, "Cos A" is taken as an example to represent the other trigonometric terms "sin A" and "tan A" as well).

The meaning of Cos A is a measure of the length of the horizontal base taking the hypothenus slanted side as reference. This is a static measurement.

Another meaning of this Cos A is the profile the term creates with change in time.

Angle A can be represented in the form 2pft.
Look at this post for details in angle presentation.

Cos A measures the height of an object taking frequency (and time) into consideration. (Dynamic measurement).

Depending on which instant of time this measurement is taken, the height may differs. It is this difference in height with time that forms a profile we call "sinusoidal" waveform.

In the frequency domain plot of KCos A, we can actually see that this term is used to represent the element of frequency (f) as well as height or amplitude (K), since Cos A is also represented as Cos 2p f t.

In summary, Cos A not only represents a ratio of numbers, it carries the meaning of length and frequency information. These information has useful applications in the field of engineering.

To quote a few examples, it is used in speech analysis (multiple vocal tone computation) and in civil engineering where determining the length or height of construction structures are very common.

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