Final answer:
A sinusoid is a function that oscillates between two values over a period of time. The given functions can be analyzed to determine if they are sinusoids. Hence, option C is correct.
Step-by-step explanation:
A sinusoid is a function that can be represented by a sine or cosine function. In other words, it is a function that oscillates between two values over a period of time.
The function 2cos(2x) is a sinusoid because it is a cosine function with an amplitude of 2 and a period of π. The function 3sin(2x) is also a sinusoid because it is a sine function with an amplitude of 3 and a period of π. The function 3sin(2x)+2cos(2x) and the function 3sin(3x)+2cos(2x) are both sinusoids because they can be written as a combination of sine and cosine functions.
The function sin(3x+3)+cos(3x+2) is NOT a sinusoid because it cannot be written as a combination of sine and cosine functions. It has a period of 2π/3 and a non-constant amplitude, which means it does not follow the definition of a sinusoid.