# How do you find the period of y= -4 cos 2x?

$\pi$
Let us look at a more general problem: $f \left(x\right) = A \cos \left(n x\right)$. In this case, we have $f \left(x + 2 \frac{\pi}{n}\right) = A \cos \left(n \left(x + 2 \frac{\pi}{n}\right)\right) = A \cos \left(n x + 2 \pi\right) = A \cos \left(n x\right)$. Try this also for $\sin$; it is exactly the same.
Thus we see that the period of such a general function is $\frac{2 \pi}{n}$.
Therefore for $f \left(x\right) = - 4 \cos \left(2 x\right)$, the period is $\frac{2 \pi}{n} = \frac{\cancel{2} \pi}{\cancel{2}} = \pi$.