Answer:
The given function is k(t) = cos(2πt/3).
The general form of a cosine function is A*cos(Bx - C) + D, where:
- A is the amplitude
- B is the frequency (which is related to the period)
- C is the phase shift
- D is the vertical shift
Comparing this form to the given function, we can see that:
- The amplitude of k(t) is A = 1, since the maximum value of the cosine function is 1 and the minimum value is -1.
- The frequency of k(t) is B = 2π/3, since the argument of the cosine function is 2πt/3. The frequency is related to the period T by the formula T = 2π/B. Therefore, the period of k(t) is T = 3.
- The phase shift of k(t) is C = 0, since there is no horizontal shift in the argument of the cosine function.
- The vertical shift of k(t) is D = 0, since the average value of the cosine function over one period is zero.
Therefore, the amplitude of k(t) is 1, the period of k(t) is 3, the phase shift of k(t) is 0, and the vertical shift of k(t) is 0.