Final answer:
The equation of a cosine wave with an amplitude of 3/4 and period of 4π/3 is y = (3/4) cos((3/2)x - (3/2)t).
Step-by-step explanation:
The equation of a cosine wave is given by y = A cos(kx - wt), where A is the amplitude, k is the wave number, and w is the angular frequency. Given the amplitude of 3/4 and period of 4π/3, we can calculate the values of A, k, and w. Since the period is equal to 2π/w, we have 4π/3 = 2π/w which gives us w = 3/2. The amplitude A is equal to |A|, so we have A = 3/4. The wave number k can be found using the relation k = 2π/λ, where λ is the wavelength. Since the period is equal to 2π/k, we have 4π/3 = 2π/k and k = 3/2.
Substituting these values into the cosine equation, we get y = (3/4) cos((3/2)x - (3/2)t).