Question about Complex Numbers: Trigonometric Form
Subject Mathematics
Mathematics
Source Originais Teachy
Originais Teachy
Topic Complex Numbers: Trigonometric Form
Complex Numbers: Trigonometric Form
Difficulty Hard
Hard
(Originais Teachy 2023) - Question Hard of Mathematics
Consider the following engineering problem: An electrical signal in a circuit can be modeled by a sine function that varies over time. To analyze the amplitude and phase of this signal, it is necessary to convert the sine function from the time domain to the frequency domain, which is represented by complex numbers in trigonometric form. If the electrical signal is modeled by f(t) = 3sin(2t + π/6), determine the corresponding complex number for f(t) in the frequency domain, represent it in trigonometric form, and discuss what the amplitude and phase of the signal physically represent. Additionally, explain how adding a constant 'a' in the argument of the sine, that is, f(t) = 3sin(2t + π/6 + a), affects the complex number in the frequency domain.Answer sheet:
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