Two transverse sinusoidal waves combining in a medium are described by the wave functions

y$1=1\mathrm{.}00$ sin$[($x $+0\mathrm{.}500$t$)]$y$2=1\mathrm{.}00$ sin$[($x $0\mathrm{.}500$t$)]$

where x$,$ y$1,$ and y$2$ are in centimeters and t is in seconds. Determine the maximum transverse position of an element of the medium at the following positions.

$($a$)$ x $=0\mathrm{.}180$ cm

$|$ymax$|=$ cm

$($b$)$ x $=0\mathrm{.}420$ cm

$|$ymax$|=$ cm

$($c$)$ x $=1\mathrm{.}40$ cm

$|$ymax$|=$ cm

$($d$)$ Find the three smallest values of x corresponding to antinodes. $($Enter your answers from smallest to largest.$)$

cm cm cm