Correct! The arguments of all transcendental functions (sin, cos,
ln, etc.) must be pure numbers.
Therefore bt has no units. The dimensions of b must be T^{-1} and
its units: s^{-1}.

Now examine the whole function:
E = al sin bt
The dimensions of sin bt are:

(a) T (b) T^{-1} (c) Transcendental functions are
dimensionless.