Final answer:
The period of the function cos((4x+9)/5) is found using the formula T = 2π / B, yielding a period of 5π / 2.
Step-by-step explanation:
To find the period of the function cos((4x+9)/5), we need to understand the general form of a cosine function, which is A cos(Bx + C) where A is the amplitude, B affects the period, and C represents the phase shift. For a cosine function, the period T is found using the formula T = 2π / B. In our case, B = 4/5, which means that the period of cos((4x+9)/5) is T = 2π / (4/5), or T = 5π / 2. This gives us the period of the function.