Wave is traveling in positive direction
Clearly, the amplitude $A=0.2$ and wavelength $\lambda =5$ and time period $T=\frac 12$
So $k=\frac{2\pi}{\lambda} = \frac{2\pi}{5}$
And $\omega =\frac{2\pi}{T} =4\pi$
So $$y=0.2 \sin (\omega t -kx \pm \phi)$$ $$y=0.2 \sin (4\pi t-\frac{2\pi x}{5} +\phi)$$
Now I have a problem with the phase of the way. I think it should be $\frac{\pi}{2}$
So $$y=0.2 \cos (4\pi t -\frac{2\pi}{5} x )$$
But the given answer is $y=0.2 \cos (\frac{2\pi x}{5} - 4\pi t)$
What is the right way to do this?
Recall that $\cos$ is an even function
$$ \cos (-z) = \cos (z) \tag{1} $$
which means
$$ 0.2\cos\left(4\pi t - \frac{2\pi}{5}x \right) = 0.2\cos\left[-\left(-4\pi t + \frac{2\pi}{5}x \right)\right] \stackrel{(1)}{=} 0.2 \cos\left(\frac{2\pi}{5}x - 4\pi t \right) $$