You are correct that Airtable currently does not have formula functions for trig.
Some additional considerations for the script ... - do you want the script to run off an automation, interface button, button field, or something else? - do you want the script to process only a triggering record, or all the records in a view? - do you want the script to calculate only sine/cosine and have a formula do the rest? Or do you want the script to calculate X. - are your angles entered in radians or degrees? (If they are degrees, you will need to convert to radians.) - can you provide sample data, including all inputs and expected outputs?
It's unfortunate that we can't do such calculations within a Formula Field. Definitely post a suggestion to Airtable support requesting such features, I think they'd be overly useful.