Final answer:
The period of a sinusoidal function is the time it takes to complete one cycle, calculated using the formula T = 1/f = 2π/ ω. For a sine wave, one cycle is 2π radians.
Step-by-step explanation:
The period of a sinusoidal function is the time it takes for one complete cycle of the wave to occur. In the context of an alternating current (AC) voltage, which is sinusoidal, as well as mechanical waves such as those on a string, the time to complete one cycle is referred to as the period (T). The relationship between the period (T), frequency (f), and angular frequency (ω) is given by the formula T = 1/f = 2π/ ω. The angle in radians for a single oscillation for a sine wave is 2π radians, meaning it goes through its full range of motion from +1 to -1 in this angle.
When modeling a sinusoidal wave as a function, you can use different equations such as y (x, t) = A sin (kx - ωt + φ) or y (x, t) = A cos (kx - ωt + φ), where A represents amplitude, k is the wave number (k = 2π/λ), ω represents the angular frequency, and φ indicates any phase shift. The motion of the wave can also be described based on its constant velocity, which relates to these quantities.