## Thursday, 14 August 2008

### Trigonometry | Parameters of Wave

A trigonometric function (for example, sinewave) can be represented by the expression
A sin (2 p f t + K).

In this expression, 3 parameters are needed to define its properties.

The first parameter is the amplitude, represented by the letter"A" in the expression.

The second parameter is the frequency "f".

The last parameter is the phase angle "K".

Changing any of these trigonometric parameters will change the profile of the sinewave.

Let us look at one example.

Here, we will play with the amplitude parameter to see what happen to the overall shape of the basic sine wave.

To make the effect more striking, let us look at a Lifted (Raised) Sine wave given below.

Expression: 3 + sin A (example to be used)

The diagram below shows how it appears.

This is a normal sine wave with a constant (positive number) added to it for the purpose of lifting the sine wave above the usual zero reference.

Now, if we replace the amplitude (A) of the normal sine with this Raised sine, and letting the phase angle (K) be zero, the new trigonometry expression becomes
(3 + sin A) sin (2 p f t).

By filling in some numbers into the variables in the expression, we obtain the wave shown below.

NOTE: The numerical values of the "sin A" in the new expression was made very different from the "sin (2 p f t)" to have the striking effect.

From the diagram above, we see that the normal sine wave can be greatly modified to desire by changing any of the parameters of the trigonometric function.

This is the power of trigonometric mathematics.

The ability to manipulate the wave through the use of trigonometry and its parameters helps make the work of people dealing with waveforms easy.

Remark:
The waveform created in the example above with the fluctuating amplitude is a case of communication broadcasting application. It is the waveform of the Amplitude Modulation technique used to broadcast AM radio channel.

In electronic communication engineering, trigonometry plays an important role in modelling the signal for design and processing. That is one real life application of trigonometry.