To find the cost of binary search in the worst case, we can model the running time as a recurrence and then find the closed-form solution. Each recursive call to binarySearch cuts the size of the array approximately in half, so we can model the worst-case cost as follows, assuming for simplicity that $n$ is a power of two.
$T(n) = T(n/2) + 1, T(1) = 1$