Answer: 3 radians/meter.
Step-by-step explanation:
The general sinusoidal function will be something like:
y = A*sin(k*x - ω*t) + C
Where:
A is the amplitude.
k is the wave number.
x is the spatial variable
ω is the angular frequency
t is the time variable.
C is the mid-value.
The rule that we can use to solve this problem, is that the argument of the sin( ) function must be in radians (or in degrees)
Then if x is in meters, the wave-number must be in radians/meters, so when these numbers multiply the "meters" part is canceled.
Then for the case of the function:
y(x,t) = 0.1 sin(3x + 10t)
Where x is in meters, the units of the wave number (the 3) must be in radians/meters. Then the angular wave number is 3 radians/meter.