#### Answer

$T=1$

#### Work Step by Step

In this question, we are given the function $f(x)=-cos2\pi x$. Given that we are interested in finding the period of this function, it might be useful for us to make use of the formula $\frac{2\pi}{T}=b$. This formula can be used whenever we are presented with either of the functions $cos(bx)$ or $sin(bx)$. The $b$ and $T$ in the formula can be swapped interchangeably.
Keep in mind that while the function does include a negative sign in front of the $cos2\pi x$, this has no bearing on the period itself as it only works to reflect the function about the x-axis.
Using the formula, $\frac{2\pi}{2\pi}=1=T$