Trigonometry - Trigonometric Graphs and Parameters
Trigonometry - Trigonometric Graphs and Parameters
TGM Original Questions
The voltage, \(V\) (in volt, \(V\)), in an alternating current (A.C.) circuit, is given by \(V = 220 \sin(100\pi t)\), where \(t\) is the time in seconds.
- Find the amplitude, period and frequency of the voltage. Note that frequency (in hertz, \(\text{Hz}\)) is defined as the reciprocal of the period.
- Find the value of the voltage when \(t = \frac{1}{600}\) \(\text{s}\).
- Sketch the graph of \(V = 220 \sin(100\pi t)\), for \(0 \le t \le 0.05\).
- Given that the frequency is tuned to \(100\) \(\text{Hz}\), the amplitude is tuned to \(110\) \(\text{V}\), find the new expression of the voltage and sketch on the same diagram the graph of the voltage, for \(0 \le t \le 0.05\). Hence explain how the values of amplitude and frequency affect the curve.
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Answer:(i) \(\text{amplitude}=220\text{ V},\ T=\frac1{50}\text{ s},\ f=50\text{ Hz}\) (ii) \(110\text{ V}\) (iii) Sketch of \(V=220\sin(100\pi t)\) (iv) \(V=110\sin(200\pi t)\); a larger amplitude increases the vertical extent, while a higher frequency produces more cycles per second.
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