I'm reading from an electrical engineering book that some
voltage v(t) is given by:

v(t) = sin(1000*t)

where t is the time
Isn't this expression, strictly speaking, incorrect? How can we
find the sine of a time quantity? Shouldn't we have a constant
in there as well with T^-1 dimension to solve this?

For example:

v(t) = sin(1000

where k a constant with units 1/s.

v(t) = sin(1000*t)

where t is the time

For example:

v(t) = sin(1000

***k***t)where k a constant with units 1/s.