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Which of the following signals is monotonic?
  • a)
    x(t) = t3 – 2t
  • b)
    x(t) = sin(t)
  • c)
    x(t) = sin22(t) + cos22(t) – 2t
  • d)
    x(t) = log(cos(t))
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Which of the following signals is monotonic?a)x(t) = t3– 2tb)x(t...
reduces to 1 – 2t, which is a strictly decreasing function.
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Which of the following signals is monotonic?a)x(t) = t3– 2tb)x(t...


Monotonic Signal Explanation:

Monotonic signals are signals that either always increase or always decrease, without any reversals or fluctuations. Let's analyze each given signal to determine which one is monotonic.

Signal Analysis:

- x(t) = t3 – 2t: This signal is not monotonic because it contains both increasing and decreasing segments. It has a cubic term that can cause the signal to change direction.

- x(t) = sin(t): This signal is periodic and oscillates between -1 and 1 as t varies. It is not monotonic because it does not strictly increase or decrease.

- x(t) = sin^2(2t) + cos^2(2t) – 2t: This signal simplifies to 1 - 2t, which is a linear function decreasing with time. It is a monotonic signal as it always decreases without any reversals.

- x(t) = log(cos(t)): This signal is not monotonic as the logarithmic function can introduce fluctuations and changes in direction.

Conclusion:

Therefore, the signal x(t) = sin^2(2t) + cos^2(2t) – 2t is the only monotonic signal among the given options.
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Which of the following signals is monotonic?a)x(t) = t3– 2tb)x(t) = sin(t)c)x(t) = sin22(t) + cos22(t) – 2td)x(t) = log(cos(t))Correct answer is option 'C'. Can you explain this answer? for Electrical Engineering (EE) 2026 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Which of the following signals is monotonic?a)x(t) = t3– 2tb)x(t) = sin(t)c)x(t) = sin22(t) + cos22(t) – 2td)x(t) = log(cos(t))Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following signals is monotonic?a)x(t) = t3– 2tb)x(t) = sin(t)c)x(t) = sin22(t) + cos22(t) – 2td)x(t) = log(cos(t))Correct answer is option 'C'. Can you explain this answer?.
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