Periodic Functions Math Example 2

Solution

1. 1
   The standard cosine $\cos(x)$ has period $2\pi$. When the argument is $3x$, the period is compressed by a factor of $3$.
2. 2
   Set $3x = 2\pi$ to find when one full cycle completes: $x = \frac{2\pi}{3}$.
3. 3
   One complete cycle of $g(x) = \cos(3x)$ occurs on the interval $\left[0, \frac{2\pi}{3}\right]$. The function starts at $g(0)=1$, reaches $-1$ at $x=\frac{\pi}{3}$, and returns to $1$ at $x=\frac{2\pi}{3}$.