Answer
The positions of the nodes are $x = \frac{4n}{3}~meters$, where $n = 1, 2, 3,...$
The positions of the anti-nodes are $x = \frac{4n+2}{3}~meters$, where $n = 0, 1, 2, 3,...$
Work Step by Step
We can find the positions of the nodes, which occur when $sin(kx) = 0$:
$sin(kx) = 0$
$kx = arcsin(0)$
$kx = n~\pi$, where $n = 1, 2, 3,...$
$x = \frac{n~\pi}{k}$, where $n = 1, 2, 3,...$
$x = \frac{n~\pi}{0.750~\pi~rad/m}$, where $n = 1, 2, 3,...$
$x = \frac{4n}{3}~meters$, where $n = 1, 2, 3,...$
We can find the positions of the anti-nodes, which occur halfway between the nodes. The first anti-node is at $x = \frac{2}{3}~m$, and the distance between each successive anti-node is $\frac{4}{3}~m$. We can find the positions of the anti-nodes:
$x = \frac{2}{3}+\frac{4n}{3}~meters$, where $n = 0, 1, 2, 3,...$
$x = \frac{4n+2}{3}~meters$, where $n = 0, 1, 2, 3,...$
