If it did sound that way, thats okay because I know what the intent was for saying it anyways.
===
If the question presents itself exactly as that, where you substitute t as a value in milliseconds, and get a value v that is in terms of cm/s, that is okay because its just a lazy book that is oversimplifying the equation...
first, cos is a dimensionless function that will return a value of -1 to 1 only, so to have a function v(t) give a value that has any dimensions, it must involve a term with dimensions. In this case, the 90 would probably be "90 cm/s" so that whatever cos evaluates to, that times 90cm/s gives you the velocity in terms of cm/s
Second, the argument for cos is also dimensionless (well, radians, but the pi carries that ..) -- there is no such thing as cos( 3 seconds) or cos( 11 hours) or cos (7s^-1) So something must turn the time-domain parameter into a dimensionless entity, in this case, the 0.3t part does that, and would likely convey "0.3 per ms", so that a value t expressed in ms such as 3ms would give you 0.1
They simply dropped the dimensions here in favor of a form stating "use the numbers directly in each spot as if unitless, we have you covered" unfortunately, but in real, physical description of any system, an equation would have dimension-cancelling constants that make it make more sense.
