Comment by don-bright

The other thing it can give you is computationally exact results since rationals are closed over division. Sine is interesting because where the input is rational the output is almost always irrational and where the output is rational the input is almost always irrational. In computation the first time you use sine in a program you have injected approximation. If you want to build things like reproducible code and geometric caching it can be interesting to compare using a purely rational computation system to an approximative system.