A progressive wave $y = A \sin (kx – \omega t)$ is reflected by a rigid wall at x = 0. Then the reflected wave can be represented by

$yz A \sin (kx – \omega t)$ for the wave progressing along the x axis and for the reflected wave,$y\text{'}= A \sin (kx + \omega t).$ But the position of the rigid wall is at x = 0. 

$\therefore$ For the given wave, its reflected wave
$y \text{'}= – A \sin (kx + \omega t).$