Question

What is the period of the following signal, \( x(t) = \sin(18\pi t + 78^\circ) \)?

• A. \( \frac{1}{9} \)
• B. \( \frac{1}{3} \)
• C. \( \frac{2}{9} \)
• D. \( \frac{4}{9} \)

Hint:

For sinusoidal signals, the period \( T \) is found using \( T = \frac{2\pi}{\omega} \), where \( \omega \) is the angular frequency.

Answer 1

The Correct Option is A

The given signal is \( x(t) = \sin(18\pi t + 78^\circ) \), where the angular frequency \( \omega = 18\pi \). The period \( T \) of a sinusoidal signal is given by: \[ T = \frac{2\pi}{\omega} \] Substituting \( \omega = 18\pi \): \[ T = \frac{2\pi}{18\pi} = \frac{1}{9} \] Thus, the period of the signal is \( \frac{1}{9} \). Therefore, the correct answer is option (1).