Brendan Burr BTEC National Certificate in ElectronicsApplied Trigonometric Techniques

Task 11.1 An alternating current waveform is given by amps.

(a) Produce a graph of 1 complete cycle of the AC waveform using Graphmatica.

Attached

(b) Give a brief description of the following and use the graph to determine their values:(i) Amplitude

The Amplitude is the maximum value of the waveform measured on the y axis. It can also be called the Peak value and is labelled as either VMax or VPeak.The VMax on the above graph is 200 Volts.

(ii) Periodic Time

The Periodic Time is the amount of time it takes to complete one cycle of the waveform. It is measured in Time (seconds) and is measured along the x axis.The Periodic Time for the above graph is 0.021 Seconds or 21 milli Seconds.

(iii) Frequency

The Frequency is the amount of cycles in one complete second. It is measured in Hertz (Hz) and can be worked out using the Periodic Time.The Frequency for the above graph is:

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Brendan Burr BTEC National Certificate in ElectronicsApplied Trigonometric Techniques

1.2 Simplify the following using the compound angle formulae.

(a)

Substitute A for Theta and B for 2700

(b)

Substitute A for Theta and B for 900

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Brendan Burr BTEC National Certificate in ElectronicsApplied Trigonometric Techniques

1.3 Verify the results in 1.1 using a suitable value for .

Using the Compound Angle Formulae:

We Get:

If we say and then:

So:

However

So

Also

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Brendan Burr BTEC National Certificate in ElectronicsApplied Trigonometric Techniques

As

Then:

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Brendan Burr BTEC National Certificate in ElectronicsApplied Trigonometric Techniques

Task 22.1 The following two voltage waveforms of the same frequency are

combined as follows:

(a) Produce a graph of one complete cycle for the voltage v using Graphmatica.

Attached

(b) Using compound angle formula, determine the resultant waveform.

(c) Produce a graph of the resultant waveform in (b) and verify the results are the same in (a).

Attached

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