Voltage of an Electrical Circuit The voltage E in an...

Voltage of an Electrical Circuit The voltage $E$ in an electrical circuit is modeled by $$E=5 \cos 120 \pi t$$ where $t$ is time measured in seconds. (a) Find the amplitude and the period. (b) Find the frequency. (c) Find $E,$ to the nearest thousandth, when $t=0,0.03,0.06,0.09,0.12$ (d) Graph $E$ for $0 \leq t \leq \frac{1}{30}$

Voltage of an Electrical Circuit The voltage $E$ in an electrical circuit is modeled by
$$E=5 \cos 120 \pi t$$ where $t$ is time measured in seconds.
(a) Find the amplitude and the period.
(b) Find the frequency.
(c) Find $E,$ to the nearest thousandth, when $t=0,0.03,0.06,0.09,0.12$
(d) Graph $E$ for $0 \leq t \leq \frac{1}{30}$

Key Concepts

Amplitude

Amplitude is the maximum absolute value of a trigonometric function from its central (mean) value. In the context of a cosine function, it is the coefficient in front of the cosine term, and it determines the peak voltage or signal strength in an electrical circuit.

Angular Frequency

Angular frequency, usually denoted by ?, represents how many radians per unit of time the sine or cosine function completes. It is used to convert time into the phase of the function and is crucial for determining the period of oscillation in periodic functions.

Period

The period of a trigonometric function is the duration required for one complete cycle of the waveform. It is calculated as the ratio of 2? to the angular frequency, indicating how long it takes for the function to repeat its pattern.

Frequency

Frequency refers to the number of cycles that occur per unit time and is the reciprocal of the period. It is a fundamental measure in oscillatory motions, especially in electrical circuits where it determines the rate of voltage or current oscillation.

Evaluating Trigonometric Functions

Evaluating trigonometric functions involves computing the function values at specific time points. This process is essential in understanding the behavior of waveforms over time and for approximating values of signals in practice.

Graphing Trigonometric Functions

Graphing trigonometric functions involves plotting the function over a specified interval to visualize its periodic behavior. Understanding the shape, amplitude, period, and phase helps in analyzing electrical signals and other oscillatory phenomena.

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