### Instruction: What is the period of $y = \cos x + \cos 2x + \cos 3x$?### Response: I want to find the smallest positive value of $x$ that makes the function repeat itself.
To do that, I need to figure out how the three cosine terms interact with each other.
I know that the period of a cosine function is $2\pi$, so the period of $\cos x$ is $2\pi$, the period of $\cos 2x$ is $\pi$, and the period of $\cos 3x$ is $\frac{2\pi}{3}$.
I also know that adding cosine functions with different frequencies can result in a function with a different period, which is called the fundamental period.
To find the fundamental period, I need to find the least common multiple of the periods of the individual terms.
The least common multiple of $2\pi$, $\pi$, and $\frac{2\pi}{3}$ is $2\pi$.
Therefore, the fundamental period of $y = \cos x + \cos 2x + \cos 3x$ is $2\pi$.