TBH you’ve possibly frightened OP *****less and got him/her thinking they need to memorise the trig tables (still got mine)...he/she only really understands the idea of SIN, COS etc.
for the benefit of Sean there’s trick sometimes called the clock code that allows you to approximate the values for the crosswind and headwind quickly.
30 minutes is
half an hour...sin of 30 is 0.5...so if the wind is 30 degrees off half of it is crosswind...
45 minutes is three quarters of an hour, sin 45 of 45 degrees is .7. (And a bit, so call it three quarters), so crosswind is 3/4 of the total.
60 minutes is the full hour, sin of 60 degrees is a bit more than .8 so it’s safe treat the full wind as crosswind.
IMHO the trick is understanding the triangle rather than memorising tables.
https://en.m.wikipedia.org/wiki/Clock_code