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To check the units of the sine argument $kx-\omega t+\phi$, assign the units of each variable: $k$ is in rad/m, $x$ is in m, $\omega$ is in rad/s, $t$ is in s, and $\phi$ is in rad. Multiply the units for $kx$ and $\omega t$ to see that meters and seconds cancel out, leaving radians.

Conditions: Applies to the traveling sinusoidal wave equation $y(x,t)=A\sin(kx-\omega t+\phi)$.; $k$ has units rad/m.; $x$ has units m.; $\omega$ has units rad/s.; $t$ has units s.; $\phi$ has units rad.

To check the units of the sine argument $kx-\omega t+\phi$, assign the units of each variable: $k$ is in rad/m, $x$ is in m, $\omega$ is in rad/s, $t$ is in s, and $\phi$ is in rad. Multiply the units for $kx$ and $\omega t$ to see that meters and seconds cancel out, leaving radians.

Conditions: Applies to the traveling sinusoidal wave equation $y(x,t)=A\sin(kx-\omega t+\phi)$.; $k$ has units rad/m.; $x$ has units m.; $\omega$ has units rad/s.; $t$ has units s.; $\phi$ has units rad.